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112 articles trouvés pour ce sujet.
Derivées partielle 1999-10-19
Arnaud Flandin pose la question :
Quel est la definition des derivées partielle
Claude Tardif lui répond.
The derivative of f(x)=2^x/x 2017-11-28
Chhavi pose la question :
Find f'(x).

Penny Nom lui répond.
Heat equation 2017-11-23
Max pose la question :
What does du\dt=a(triangle)^2u mean. Can it be solved for t.
Penny Nom lui répond.
A tangent to a curve 2017-10-22
Jasem pose la question :

Suppose that

(A) Find an equation for the tangent line to the graph of f(x) at x=2

(B) Find all values of xx where the tangent line is horizontal, and enter them as a comma-separated list (e.g., 2,-3,6). If there are none, enter none.

Values of x

Penny Nom lui répond.
The derivative of the inverse of a function 2016-10-28
Kate pose la question :
Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^-1(4) if f(3)=4 and f'(3)=1/7

Penny Nom lui répond.
Implicit differentiation 2016-06-06
Pranay pose la question :
Is a circle x^2+y^2=2 a function? If it is not a function, why is it possible to do implicit differentiation on it?

Penny Nom lui répond.
The derivative of x! 2016-04-16
Sang pose la question :
How to find the derivative of x! and integral of x!
Penny Nom lui répond.
A tangent line to a parabola 2015-12-02
pei pose la question :
Given that the line y=mx-5 is a tangent to the curve y=2x^2+3 find the positive value of M.
Penny Nom lui répond.
The derivative of x^1/3 2015-11-08
omar pose la question :
hi can help me
am teacher ask me about x^1/3 Derivation definition .

Penny Nom lui répond.
Two cars approaching an intersection 2015-04-16
Engabu pose la question :
Car A is traveling west at 50km/h & car B is traveling north at 60km/h. both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 3km & car B is 4km from the intersection?
Penny Nom lui répond.
Constructing a box of maximum volume 2015-04-14
Margot pose la question :
I need to do a PA for maths and I'm a bit stuck. The PA is about folding a box with a volume that is as big as possible. The first few questions where really easy but then this one came up.

8. Prove by differentiating that the formula at 7 does indeed give you the maximum volume for each value of z.

Penny Nom lui répond.
Differentiate ln[x(2x-4)^1/2] 2014-06-28
Igwe pose la question :
If y=In[x(2x-4)^1/2],find dy/dx at x=3
Penny Nom lui répond.
The derivative of sin(x) 2014-04-26
Lucky pose la question :
f(x)=Sin(x), by first principle its f'(x)...show me how to solve such problem.
Penny Nom lui répond.
The domain of a derivative 2013-10-10
Renee pose la question :
I am looking to find the domain of a derivative of a radical function, one such as: f(x) = the square root of (8 − x).
I am kind of unclear on how domains work for derivative. I don't understand how you take a function's domain and use that to find the derivative's domain.

Penny Nom lui répond.
Equal ordinate and abscissa 2013-08-15
sonit pose la question :
the slope of tangent to the curve y=(4-x^2)^1/2 at the point, where the ordinate and abscissa are equal, is
Penny Nom lui répond.
Distance as a function of acceleration 2013-07-10
Tom pose la question :
If you start at a stoplight and your acceleration is 16t - t^2, how far have you gone after 8 seconds?
Penny Nom lui répond.
f(x) + f ''''(x)=0 2013-03-05
Andreea pose la question :
Hei. I don’t speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something.
Brennan Yaremko lui répond.
The derivative of y = sin (30º + x) 2012-11-07
Saskia pose la question :
derivative of y = sin (30º + x)
Harley Weston lui répond.
Differentiation rules 2012-10-23
Morgan pose la question :
Use the derivative rules to differentiate each of the following:
1. f(x)=1/x-1
2. f(x)= sqrt(x)

Penny Nom lui répond.
The derivative of 2sin cubed x - 3 sin x 2012-03-25
holly pose la question :
suppose f(x) = 2sin cubed x - 3 sin x

show that f 1(x) = -3 cos x cos 2x

Harley Weston lui répond.
Integral 1/(25-x^2)^3/2 2012-02-22
John pose la question :
Integral 1/(25-x^2)^3/2
Harley Weston lui répond.
Dt[sin t tan (t^2+1)] 2012-02-21
Ayu pose la question :
Dt[sin t tan (t^2+1)]

Harley Weston lui répond.
Notation for the second derivative 2012-02-06
Shafira pose la question :
In all math textbooks, it is written that d/dx ( d/dx) (y)= d2y/dx2. Why do they write it as d2y/dx2, not as d2y/d2x2?
Robert Dawson lui répond.
The derivative of x^-(1/2) 2012-01-14
Eric pose la question :
I have an problem figuring out the derivative of the negative square root of x i.e. x^-(1/2) using the first principle.
Could someone please show me?
Thanks in advance!

Harley Weston lui répond.
Implicit differentiation 2011-10-20
Monica pose la question :
Find dy/dx in terms of x and y, if sin(xy)=(x^2)-y.
Penny Nom lui répond.
The derivative of f(x) = (x+1)^1/2 2011-09-05
Carla pose la question :
Find the derivative using the limit process of
f(x) = (x+1)^1/2

Harley Weston lui répond.
An antiderivative of the square root of (8t + 3) 2011-04-19
Caitlyn pose la question :
I know how to take an antiderivative. But this one's stumping me. I need it to finish a problem. What's the antiderivative of the square root of (8t + 3)


Penny Nom lui répond.
A stone is dropped into a lake 2011-03-24
AnneMarie pose la question :
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 25 cm/s. Find the rate at which the area within the circle is increasing after 4s.
Penny Nom lui répond.
The integral of (x^2*exp(x)/(exp(x)-1)^2 2010-08-09
sujoy pose la question :
please find this integral for me


Robert Dawson lui répond.
Using the limit definition 2010-06-06
Meagan pose la question :
Using the limit definition find the derivative of 3/(2x^2)
Harley Weston lui répond.
The derivative of y=x^x 2010-04-09
David pose la question :
So, its David, and I was wondering about the derivative of y=x^x. I have often seen it be shown as x^x(ln(x)+1), but when I did it through limits it turned out differently. Here's what I did:
It is commonly know that df(x)/dx of a function is also the limit as h->0 of f(x+h)-f(x)/h. To do this for x^x you have to start with lim h->0 ((x+h)^(x+h)-x^x)/h. The binomial theorem then shows us that this is equal to lim h->0 (x^(x+h)+(x+h)x^(x+h-1)h+...-x^x)/h
This is also equal to lim a->0 lim h->0 (x^(x+a)+(x+h)x^(x+h-1)h...-x^x)/h.
Evaluating for a=0 you get lim h->0 (x^x+(x+h)x^(x+h-1)h...x^x)/h
Seeing as the last 2 terms on the numerator cancel out you can simplify to a numerator with h's is each of the terms, which you can then divide by h to get:
lim h->0 (x+h)x^(x+h-1)... which when evaluated for h=0 gives us: x(x^(x-1)). This statement is also equal to x^x.
This contradicts the definition of the derivative of x^x that is commonly shown. So, my question is: can you find any flaws in the logic of that procedure? I do not want to be shown how to differentiate x^x implicitly because I already know how to do that.

Robert Dawson lui répond.
The derivative of cos^3x 2010-04-06
Erson pose la question :
Find y' of the given function: y = cos^3x.
Harley Weston lui répond.
The second derivative of y = x³ (x² + 5) 2009-12-14
Kyrie pose la question :
Find d²y/dx² for this function:

y = x³ (x² + 5)

Penny Nom lui répond.
Graphing y=(4-x^2)^5 2009-10-25
natalie pose la question :
I want to graph the curve of y=(4-x^2)^5 without using a graphing calculator. To do this, I'm suppose to find: domain, y and x intercepts, asymptotes, intervals of increase/decrease, local max/min, concavity and points of inflection. I got all the way to the step where I'm solving the concavity and I'm stuck. I found the f"(x) and it came out to be really large polynomial. I want to know how I can solve for the x of f"(x) without the use of a graphing calculator, when the polynomial has x^6 and x^8. Thank you so much, natalie
Harley Weston lui répond.
Differentiating y= square root(x-1) 2009-09-29
edith pose la question :
describe the x-values at which f is differentiable.
y= square root(x-1)

Penny Nom lui répond.
An antiderivative problem 2009-08-13
Indrajit pose la question :
∫4e^x + 6e^-x/(9e^x + 4e^-x)dx = Ax + Bloge(9e2x - 4) + C

then A=?......B=?.....C=?

plz solve it...."^" stands for "to the power of"....

Harley Weston lui répond.
Application of Derivatives of Trig Functions 2009-05-21
Alannah pose la question :
I have a word problem from my Calculus textbook that I can't figure out. Triangle ABC is inscribed in a semicircle with diameter BC=10cm. Find the value of angle B that produces the triangle of maximum area. I am supposed to set up an equation for the area of the triangle A=b x h/2 using Trig functions based on angle B to represent the base and height but I'm not sure how to do this when the side length given is not the hypotenuse.
Janice Cotcher lui répond.
The derivative using limits 2009-04-21
Kirstin pose la question :
I am trying to take the limit of f(x) = [f(x+h)-f(x)] / h If you try taking the limit by substituting the limiting value h=0, you get 0/0, which of course is not the right answer. You rewrite f(x+h)-f(x) so it has a factor of h in it, which you cancel with the h in the denominator before you substitute h=0. But I am not sure how to do this. Thanks.
Robert Dawson lui répond.
The second derivative of h(x)=f(g(x)) 2009-02-16
Kristina pose la question :
If h(x)=f(g(x)), and is differentiable, then find h"(x).
Robert Dawson lui répond.
A definite integral 2009-02-09
Mathata pose la question :
Evaluate: integral from 0 to 1, x^2 e^x^3dx
Harley Weston lui répond.
What's the derivative of y = e^2x-e^-2x / e^2x+e^-2x? 2009-02-02
Heather pose la question :
What's the derivative of y = e^2x-e^-2x / e^2x+e^-2x ?
Harley Weston lui répond.
Partial derivatives 2009-01-17
Meghan pose la question :
I have a question I've been working at for a while with maxima/minima of partial derivatives.

"Postal rules require that the length + girth of a package (dimensions x, y, l) cannot exceed 84 inches in order to be mailed. Find the dimensions of the rectangular package of greatest volume that can be mailed. (84 = length + girth = l + 2x + 2y)"

Harley Weston lui répond.
Negative rate of change 2009-01-12
hemanshu pose la question :
when i have to find rate of change of decrease in any value my ans comes in negative why??????????
Penny Nom lui répond.
Determine y'' by implicitly differentiating twice 2009-01-04
Walter pose la question :
Given x^3 - 3xy + y^3 = 1 , determine y'' by implicitly differentiating twice. I cannot solve this. Would you be kind enough to perform the mathematics and show the steps involved in obtaining the solution?
Harley Weston lui répond.
Antiderivative of 1/(x(1 - x)) 2008-10-22
Matt pose la question :
derivative of dx/(x(1-x))

From what I've seen I should break apart the equation as such derivative of dx/x - dx/(1-x) and then get the 2 corresponding log functions.

If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative.

Harley Weston lui répond.
Concavity and the second derivative 2008-10-15
Christina pose la question :
I'm having trouble solving for a second derivative for the following graphing question.

f(x) = (X^2+2x+4)/2x

using the quotient rule, I found:
f'(x) = (x^2-4)/(2x^2)

however, using the quotient rule again I can't seem to solve it (concavity):
f''(x)=[(4x^3-(4x^3 -16x)]/4x^4

and making the equation equal to zero result in 0=4 which doesn't seem to make sense...

Penny Nom lui répond.
What is the derivative of (2^sinx)/(logbase4(2x+1))? 2008-09-16
Jesse pose la question :
What is the derivative of (2^sinx)/(logbase4(2x+1))
Harley Weston lui répond.
f(x)=sin^3(3x^2) find f ' (x) 2008-04-21
Michael pose la question :
f(x)=sin^3(3x^2) find f ' (x)
Harley Weston lui répond.
f(x) =ax^blnx 2008-04-13
charles pose la question :
supposef(x) =ax^blnx is a real- valued function. Determine exact values(not decimal approximations) fro nonzero constants a and b so that the function f has a critical point at x=e^3 and a maximum value of 1/2e
Harley Weston lui répond.
The chain rule 2008-04-10
joey pose la question :
pls help me to Differentiate

Harley Weston lui répond.
Differentiate 2007-12-28
taiwo pose la question :
i am finding it difficult to use first principle to differentiate this question: y=xcos2x. can u help me.
Penny Nom lui répond.
A curve sketch 2007-11-22
Ahson pose la question :
Find critical points, determine the monotonicity and concavity and sketch a graph of f(x) with any local maximum, local minimum and inflection points labeled:

1. f(x) = x^4 - x^3 - 3x^2 + 1

Harley Weston lui répond.
The derivative 2007-11-19
ralf pose la question :
Find the derivative of the function
1-. y=1+2x8
2-. y=(1+2x )8

Harley Weston lui répond.
f(x+y) = f(x) + f(y) + 2xy 2007-11-01
Marcia pose la question :
For all real numbers x and y, let f be a function such that f(x+y) = f(x) + f(y) + 2xy and such that the limit as h -> 0 of f(h) / h = 7, find: f(0), use the definition of the derivative to find f'(x), and find f(x).
Penny Nom lui répond.
How to solve related rates problems 2007-10-27
David pose la question :
Can you plz explain how and where you come up with an equation to solve this?
Find the rate of change of the distance between the origin and a moving point on the graph of y = sin x if dx/dt = 2 centimeters per second.

Stephen La Rocque lui répond.
The derivative of f(x)=1/(x-1) 2007-09-21
Michelle pose la question :
im having trouble finding the derivative of f(x)=1/(x-1) using the f(x+h)-f(x)/h method.
Stephen La Rocque lui répond.
Differentiate x^(1/3) using first principles 2007-09-14
Sheila pose la question :
our teacher gave us this question as a challenge and even he couldnt figure it out: Differentiate x^(1/3) [aka the cube root of x] using first principles. i know the answer is 1/(3.x^2/3), but how is it possible using first principles?
Harley Weston lui répond.
Using the chain rule to solve a derivative 2007-07-29
Charles pose la question :
I need to find the derivative fo the following function.   _______________________
\/ ______________
  \/ (x - 1) / (x + 2) + 1

Stephen La Rocque lui répond.
Implicit Derivatives 2007-07-13
Charles pose la question :
I need help computing y' by implicit differentiation the question is: y^2 + x/y + 4x^2 - 3
Stephen La Rocque lui répond.
Derivative of a Function 2007-07-09
Bob pose la question :
What is the derivative of the function a sub n = [n/(n+1)]^n ?
Stephen La Rocque lui répond.
Log base 2 of log base 2 of x 2007-06-27
alex pose la question :
y = log base 2 of lag base 2 of x The slope of the tangent to the given curve at its x-intercept is..?
Harley Weston lui répond.
Maximizing the volume of a cone given the slant length 2007-05-14
Christina pose la question :
A coffee filter for a new coffee maker is to be designed using a conical filter. The filter is to be made from a circle of radius 10cm with a sector cut from it such that the volume of coffee held in the filter is maximised. Determine the dimensions of the filter such that the volume is maximised.
Stephen La Rocque and Kerstin Voigt lui répond.
The second derivative 2007-04-14
Gerry pose la question :
In mathematical context,what do you understand by the term "Second Derivative"
Penny Nom lui répond.
y = sin(2x) 2007-03-22
bader pose la question :
sin(2x) find dx/dy
Penny Nom lui répond.
Derivatives 2007-02-01
Jacob pose la question :
Find the derivative of: y= pi^2+x^2+3xy+sin(y^2)
Penny Nom lui répond.
Differentiate Y= sin3x + cos7x 2006-08-22
james pose la question :
Differentiate the function of x using the basic rules.

Y= sin3x + cos7x

Stephen La Rocque lui répond.
livinia the housefly finds herself caught in the oven 2006-06-27
Danielle pose la question :

livinia the housefly finds herself caught in the oven at the point (0,0,1). the temperature at the points in the oven is given by the function

T(x,y,z) = 10 (xe(-y2) + ze(-x2))

where the units are in degrees celsius.

(i.)so if livinia begins to move towards the point (2,3,1) at what rate in deg/cm does she find the temp. changing?
(ii.)in what direction should she move in order to cool off as rapidly as possible?
(iii.)suppose that livinia can fly at a speed of the square root of 2 (cm/sec.) if she moves in the direction of part (ii) at what rate will she find the temp. to be changing?

Penny Nom lui répond.
differentiate the volume of a cylinder with V respect to h 2006-05-24
A student pose la question :
differentiate the volume of a cylinder with V respect to h
Stephen La Rocque lui répond.
Rate of ladder falling 2006-04-30
Harsh pose la question :
A ladder 4 m long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 30 cm/s, how quickly is the top of the ladder sliding down the wall when the bottom of the ladder is 2 m from the wall?
Stephen La Rocque lui répond.
Differentiation, powers and logs 2006-01-06
Claudia pose la question :

Question: how do I find the derivative of

x* ln(x+(e^2))^2



Penny Nom lui répond.
Notation for the second derivative 2005-11-08
Mussawar pose la question :
my question is d/dx( dy/dx) = d2y/dx2. why it is not equal to d2y/d2x.
Penny Nom lui répond.
Velocity and acceleration 2005-10-27
Candace pose la question :
When taking the integral of the position function, you get the velocity function, and the same for velocity to acceleration. So when you do each of these, you get a function. But when you integrate on a graph, you get an area under a curve. The area is un units squared- where do the units go when you make it an equation? How can a function be an area?
Harley Weston lui répond.
Can we take the derivative of independent variable 2005-10-18
Mussawar pose la question :
why we take derivative of dependent variable with respect to independent variable .can we take the derivative of independent with respect to dependent.if not why.
Walter Whiteley lui répond.
How do you differentiate y=(x)^(x^x)? 2005-09-14
Calebius pose la question :
How do you differentiate y=(x)(xx)?
Penny Nom lui répond.
Differentiating F(x,y) = 0 2005-01-23
Jacob pose la question :
In calculus, we often mention to the students that if F(x,y) = 0, then we can differentiate both sides and still get an equality. The problem is that we can't perform the same operation on F(x) = 0, say x = 0, otherwise 1 = 0, which is absurd. What is the reason?
Walyer Whileley and Harley Weston lui répond.
ln(x)/x 2004-12-11
Tina pose la question :
What is the derivative of (ln x)/x? The double derivative?
Penny Nom lui répond.
The third derivative 2004-10-15
Holly pose la question :
Why would you ever take the third derivative?
Harley Weston lui répond.
differentiate Y=X^X^X 2004-09-13
Kunle pose la question :
differentiate Y=X^X^X
Penny Nom lui répond.
Differentiation 2004-08-04
A parent pose la question :
I am a parent trying to understand higher level of maths and would be very grateful if you could help with differentiating the following functions, identifying general rules of calculus:

a) f(x)=e^2^xIn(cos(8x))

b) f(x)=secx/SQRTx^4+1

Penny Nom lui répond.
Some calculus problems 2004-04-01
Weisu pose la question :

I have questions about three word problems and one
regular problem, all dealing with derivatives.

  1. Find all points on xy=exy where the tangent line
    is horizontal.
  2. The width x of a rectangle is decreasing at 3 cm/s,
    and its length y is increasing at 5 cm/s. At what rate
    is its area A changing when x=10 and y=15?
  3. A car and a truck leave the same intersection, the
    truck heading north at 60 mph and the car heading west
    at 55 mph. At what rate is the distance between the
    car and the truck changing when the car and the truck
    are 30 miles and 40 miles from the intersection,
  4. The production P of a company satisfies the
    equation P=x2 + 0.1xy + y2, where x and y are
    the inputs. At a certain period x=10 units and y=8
    units. Estimate the change in y that should be made to
    set up a decrease of 0.5 in the input x so that the
    production remains the same.

If you could just give me some hints on these
questions, I'd really appreciate it. Thanks!

Penny Nom lui répond.
A derivative 2004-03-31
A student pose la question :
What is the nth derivative of f(x) =(2x)/(1-(x2))?
Harley Weston lui répond.
A partial derivative 2004-03-19
Penny Nom pose la question :
Is it possible to differentiate the following equation, if so could you please explain.


I would like the derivative of S with respect to X.

Harley Weston lui répond.
Areas, perimeters and derivatives 2004-02-15
Geoff pose la question :
A recent lecture in my calculus class led me to realize that the derivative of the area of a circle, with respect to the radius is equal to the circumfrence. This also holds true for the relationship between the volume of a sphere and the surface area of that sphere:
why do these hold true? why is it only for circular objects?

Harley Weston lui répond.
The derivative of x to the x 2004-02-14
Cher pose la question :
what about the derivative of x to the power x?
Penny Nom lui répond.
Functions, graphs and derivatives 2003-10-05
Jathiyah pose la question :
I wanted to know how would you tell (on a graph diplaying two funtions), which funtion is the derivative of the other?
Walter Whiteley lui répond.
The slope of a tangent 2003-10-01
A student pose la question :

find the slope of the tangent to each curve at the given point

f(x)=square root 16-x, where y=5

Penny Nom lui répond.
The slope of a tangent line 2002-03-04
Ridley pose la question :
Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5).
Harley Weston lui répond.
A tangent line 2001-11-21
A student pose la question :
write an equation of the line tangent to the graph of

ey + ln(xy) = 1 + e at (e,1)

Harley Weston lui répond.
4 sinx cosy = 1 2001-10-10
A student pose la question :
How would i differentiate the following example in terms of t (x and y are functions of t)

4 sinx cosy = 1

Claude Tardif lui répond.
(x^2-5x-6)/(x-6) 2001-10-02
Bill pose la question :
given f(x) = (x2-5x-6)/(x-6) find f'(6).
Harley Weston lui répond.
Differentiation 2001-04-17
Esther pose la question :
Could you please tell me what the first derivative is of the following:

y = 2/(2x+e2x)

Is it (1+xe2x)/(2x+e2x)2 or perhaps -4(1+e2x)/(2x+e2x)2 ? I am a little confused between the two!

Harley Weston lui répond.
The domain of the derivative 2001-02-22
Wayne pose la question :
I know that the domain of f'(x) is a subset of the domain of f(x). Is it necessarily true that the subset will have at most one less element than the domain of the original function?
Harley Wesston lui répond.
Differentiation of y = x n 2001-02-17
Jashan pose la question :
i am studying differentation at the moment i have drawn some graphs such as y=x 2. i have found the formula for the gradient of this curve, this being 2x obtained by using differentation, but i need to know the general case for the formula where y=xn in order for me to understand this topic more throughly, i would also like to know how u derived this general formula
Harley Weston lui répond.
Concavity 2000-10-22
Alex pose la question :
the question is: on what interval is f(x)=(x2)(ex)?

ive found the 2nd derivative which is ex(x2+4x+2) and i did the quadratic to get -2-20.5 and -2+20.5, but i dont know what the interval is.
Harley Weston lui répond.

Derivatives, there must be an easier way 2000-09-06
Brad Goorman pose la question :
The direction read: Take the derivative of each expression.

y = {1+[x+(x2 +x3)4]5}6

Harley Weston lui répond.
A derivative problem 2000-06-04
Jeff Ellis pose la question :
If F(x)=(4+x)(3+2x2)2(2+3x3)3, find F'(0)
Harley Weston lui répond.
Thearcius Functionius 2000-05-03
Kevin Palmer pose la question :
With the Olympics fast approaching the networks are focusing in ona new and exciting runner from Greece. Thearcius Functionius has astounded the world with his speed. He has already established new world records in the 100 meter dash and looks to improve on those times at the 2000 Summer Olympics.

Thearcius Functionius stands a full 2 meters tall and the networks plan on placing a camera on the ground at some location after the finish line(in his lane) to film the history making run. The camera is set to film him from his knees(0.5 meters up from the ground) to 0.5 meters above his head at the instant he finishes the race. This is a total distance of two meters(the distance shown by the camera's lens).
Harley Weston lui répond.

An indefinite integral 2000-05-03
Bonnie Null pose la question :
I am to find the indefinite integral of: (ex - e-x)2 dx
Claude Tardif lui répond.
y = x^x^x^x... 2000-04-05
Michael Hackman pose la question :
Find the derivative of: y = x^x^x^x... on to infinity.
Claude Tardif lui répond.
A calculus problem 1999-12-08
JT Wilkins pose la question :
These are the questions:

  1. Show that there exists a unique function that meets the following requirements:

    a) f is differentiable everywhere
    b) f(0)= f'(0)= 0
    c) f(x+y)= f(x)+ f(y), for all real values of x,y

  2. Consider the function F: R-->R (All Reals)

    F(x) = 0, for x irrational & 1/q, x=p/q gcd(p,q)=1 q > 0

    a)determine the values x where f is continuous, respectively discontinuous.
    b)determine the values x when f is differentiable and for each of these values compute f'(x).

Penny Nom lui répond.
The chain rule 1999-12-03
Jennifer Stanley pose la question :
This problem is making me dizzy. I would greatly appreciate a little help!

Express the derivative dy/dx in terms of x.

y=u^2(u-u^4)^3 and u=1/x^2
Harley Weston lui répond.

Two calculus problems 1999-12-01
O'Sullivan pose la question :
Question #1 Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely? It's under the chain rule section of differentiation if that any help.

I've set up a ratio and tried to find the constant but am stuck.

Question #2 The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x^2 + 4y^2 < or= 5. If the point (-5,0) is on the edge of the shadow, how far above the x axis is the lamp located?

The picture shows an x and y axis with only the points -5 and 3 written on the x axis. the lamp is on the upper right quadrant shining down diagonally to the left. There's an ellipse around the origin creating the shadow. It's formula is given as x^2 + 4y^2=5.

Harley Weston lui répond.
Two derivatives 1999-11-16
Gina Renicker pose la question :
The derivative of:

y=e(xlnx) and y=x2arctan(x1/2)
Harley Weston lui répond.

Clockwise or Counterclockwise? 1999-10-27
Tim pose la question :
A particle moves around the circle x2 + y2 = 1 with an x-velocity component dx/dt = y
  1. Find dy/dt

  2. Does the particle travel clockwise or counterclockwise around the circle? Why?

Harley Weston lui répond.
Derivatives with logs 1999-10-26
Kate pose la question :
What is the derivative of 5 to the 5x-2 at x equals 0.8?
Harley Weston lui répond.
Parametric Equations 1999-08-06
Nicholas Lawton pose la question :
Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is :

Harley Weston lui répond.

A calculus problem 1999-07-22
Nicholas Lawton pose la question :
The curve y= e^x(px^2+qx+r) is such that the tangents at x=1 and x=3 are parallel to the x-axis. the point (0,9) is on the curve. Find the values of p,q and r.
Harley Weston lui répond.
Graphing the Derivative 1999-01-18
Milena Ghebre pose la question :
This question has been nagging me for sometime now.

Is there a way of finding out the derivative of a function, just by looking at the graph of it?
Walter Whiteley lui répond.

Calculus 1999-01-16
Kaylea Rankin pose la question :
Differentiate the following.

y = 1 /(2+3/x)
Jack LeSage and Penny Nom lui répond.

The area and the circumference of a circle. 1998-08-27
Jason Wright pose la question :
I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me!
Walter Whiteley lui répond.
A Tightrope Walker. 1998-02-19
Amy Zitron pose la question :
A tightrope is stretched 30 feet above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A....
Harley Weston lui répond.
Mathematical Induction and the Derivative 1997-03-18
Shuling Chong pose la question :
"Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n."

Any educated tries are appreciated.
Penny Nom lui répond.




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