# calculus - derivatives

16,904 results

Calculus: Derivatives
I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from? Thanks!

calculus
find the second-order partial derivatives of f(x,y)=x^3 + x^2y^2 + y^3 + x+y and show that the mixed partial derivatives fxy and fyx are equal

Math - Calculus 1
Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4 - (1.1)^2

Calculus (Derivatives)
What is the derivative of the this functon? g(x) = -500/x, x cannot equal 0. I know that in order to fnd the derivative I need to put the function into the equation for evaluating derivatives as limits. lim as h -> 0 (f(x+h) - f(x))/h I did this, but I am having ...

calculus - derivatives
can you please find the first 5 derivatives for: f(x) = (0.5e^x)-(0.5e^-x) f'(x) = ? f''(x) = ? f'''(x) = ? f''''(x) = ? f'''''(x) = ? thanks :) f(x) = (0.5e^x)-(0.5e^-x) f'(x) = 0.5 e^x + 0.5 e^-x f''(x) = 0.5 e^x - 0.5 e^-x f'''(x) = 0.5 e^x + 0.5 e^-x f''''(x) = 0.5 e^x - 0...

convert derivatives of x,y,z, to r, Ɵ,z
convert derivatives of x,y,z, to r, Ɵ,z with chain rule? I want provment rules of converting rectangular derivatives to cylindrical derivatives and and also cylindrical to spherical.I know the rules but I cant prove EQUATIONS.thx alot

math
I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you

Calculus/Derivatives
In addition, can you walk me through how to get the derivatives for these 2 statements, too? a) y = x^5/3 - 5x^2/3 b) y = (the cubed root of the quantity) [(x^2 - 1)^2] Hi there. I need to find the first derivative of this statement. y=x(x+2)^3 I tried the chain rule, but I ...

a) determine the derivative of y = sin2x b) determine the derivative of y = 2SinxCosx c) shoe that derivatives in parts a) and b) are equal d) explain why derivatives in parts a) and be should be equal.

Calculus
Find the outside and inside functions of the following to find their derivatives: 1) sqrt(2x+9) 2) cos(cos(x)) 3) tan(x) I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the outside and inside.

Calculus
show that the curves r=asin(è) and r=acos(è) intersect at right angles. can you show that the derivatives for each are the negative reciprocal of each other? That is the key. i need more info..i know how to find the derivative...but how will that prove my question. Do I need...

calculus
derivatives. f(x)=(1/-7x^12) f'(2)=? f'(-1)=?

Derivatives ~ Calculus
If dy/dx = (1 + x)/(xy), x>0, and y=-4 when x=1, then when x=3, y= what?

calculus
a)find the first partial derivatives of f(x y)= x √1+y^2 b)find the first partial derivatives of f(x,y)= e^x ln y at the point (0,e)

Calculus
Compute the derivatives of : f(x)= x^7 + 7^x+ 7^7

Calculus-derivatives
Determine h'(x) for h(x)= [x/(1-x)]^2

calculus
Anti-Derivatives 2x^6-x^3/x^2

Calculus
Apply the concepts of calculus (limits and derivatives) to describe the graph y = sec(x). Include a quality graph

Math-Derivitives

calculus
find the derivatives F(x)=8ln(x^5-2x)

calculus derivatives
Please confirm: {(5x+2)^4/x^2-3x+1)^3}= 20(5x+2)^2(x^2-3x+1)^3 -3x^2(5x+2)^4 (x^2-3x+1)^2/(x^2-3x+1)^6

calculus
Find the derivatives of the functions k(x)=(x^3+e^x)^4

Calculus (derivatives)
Find the derivative of cos^2(4x)

calculus
find the derivatives 1. y=sin^3(2x)(cos2x)

calculus
find the derivatives 1. y=sin^3(2x)(cos2x)

calculus
derivatives: 2. cos teta/ 1+sin^2

Calculus
Just got through with derivatives, power rule, and chain rule. I am supposed to find the first and second derivatives of the function. y = 4x/√x+1 and y = cos^2(x) y' = [(x+1)^(1/2)(4)]-[(4x)(1/2(x+1)^(-1/2))(1)] y' = [4(x+1)^(1/2)-4x]/[2(x+1)^(1/2)(x+1)] y' = (2-4x)/(x+...

Calculus
Find a formula for the derivatives of the function m(x)=1/(x+1) IS the answer -1/(x+h)(x+h+1)

calculus
derivatives: 3. y= cot^3(2/x) 4. y= csc^5 (1-t+3t^2) 5. y=sec(5x)/tan3x

Calculus(derivatives)
f(x)=7cosx+6tanx, find f'(x)and f'(5pie/4)

Calculus (derivatives)
find the slopes at the indicated points y = 3 + 5x - 3x^3 (0,3), (1/2, 41/8), (2,-11)

calculus
Z=square root of(x^2+y^2) + xy Find the partial derivatives: x, xx, y, yy, xy. Thanks.

Calculus
I get mixed up when graphing derivatives. If I'm given the graph of f how do I get f' and f"?

Calculus, derivatives
The curve is given by x^2+2r(sqrt(y))=xy What is dx/dr when y is constant?

Calculus, derivatives
Derivative of y=(a^x)+(x^a). Show steps, please.

calculus
find the first and second derivatives for 3x^4-4xy^2+7=2y

calculus
Find the first and second derivatives of the function. h(x) = sqrt x^2 + 1

calculus
find the partial derivatives du/dx, du/dy and du/dt. u= root (r^2+s^2, r = y + x cos(t), s = x + y sin(t);when x = 0, y = 2, t = 2

Calculus-derivatives
f(x) = (x-1)^(2/3)*(x+3) What are the critical numbers? the derivative would be =2/3(x-1)^(-1/3)(x+3) + (x-1)^2/3 What do I do next?

Calculus
Find all first partial derivatives: f(x,y)=e^(xy)cosx

Calculus-derivatives
At what points on the graph of f(x)=6x^2+4x-9 is the slope of the tangent line -2?

Calculus - Anti-Derivatives
How would you find the Integral of (cos(x\8))^3, defined from -(4 x pi)/3) to (4 x pi)/3)

calculus - (derivatives)
Find the derivative of the function f by using the rules of differentiation. F(x) = 3 ã x

Calculus First Derivatives
If f(2) = 2.5 and f'(2) = -2.5, then f(2.5) is approximately... I have no idea how to do this without an equation.

calculus/derivatives
I need to find the derivative and can't do them when they are raised to powers? Thank You. m(x)x^5 - 5x^3+7x -4)^10 (4x^9 +19)^23 this on is tuff!

Calculus - HELP plz!
Find all of the first partial derivatives of f(x,y,z)=arctan y/xz

Calculus
If F(x)=f(g(x)-h(x)), where g(3)=5, h(3)=4, g'(3)=3, h'(3)=1 and f'(1)=10, find F'(3). I know how to do derivatives and all, but I rlly can't figure this question out

Calculus
What is wrong with the following reasoning??? f(x) = 2^x f'(x) = x[2^(x-1)] Although n x^(n-1) is the derivative of x^n, you cannot apply similar rules when x is the exponent and the number being raised to a power is a constant. The derivative of b^x, where b is a constant, is...

Calculus AB (AP)
Hi, I have a calculus test tomorrow and I understand how to complete all of the problems, but I am unsure behind the reasoning of taking two derivatives. Can someone please explain the following: 1. g(x)=e^(f(x)) g'(x)=e^(f(x))f'(x) 2. f(x)=Integral from 0 to 3x of the square ...

Calculus Derivatives
what's the equations of both lines through the point (2,3) that are tangent to the parabola y=x^2+x

differential calculus
use the product rule to find the derivatives of the given function y=(3x^2-8)^2

calculus-derivatives
y=cos^3(12theta) find derivative using chain rule

Calculus (derivatives)
find an equation of the tangent line to the curve at the indicated point. y = -(x^1/3); (8, -2)

Calculus

mathematics-calculus-derivatives
. If y=cosx, find dy/d5x please show workings #thanks

Calculus
Find a formula for the derivatives of the function m(x)=1/(x+1) Please help.....Any assistance would be greatly appreciated.

Calculus-Derivatives
How is 6#sin(#x-1)/cos^3(#x-1) the derivative of f(x)= 3sec^2(#x-1)? #= Pi (I coulnd't find the symbol...sorry.)

calculus quick question
g(x)= sqrt(1-4x^2) Can someone help me find the first and second derivatives please!

Calculus-Math
Complete the table. y = f(g(x)) u = g(x) y = f(u) y = (2x − 4)^7 u = y= This problem involves the chain rule of derivatives.

mathematics-calculus-derivatives
. Try this. If y=cosx find dy/d5x please show workings #thanks

calculus
Find all first and second partial derivatives of z with respect to x and y if x^2+4y^2+16z^2−64=0.

Calculus - Derivatives
Use implicit differentiation to find the second derivative y'' of the function given. x^2 + 5y^3 = 8

Calculus (Derivatives)
Using the product rule, find the derivative of the following function: (x^1/2 cscx sinx).

Calculus: Implicit Derivatives
Compute d/dx[f(g(x))] -where f(x)=x^4-x^2 -and g(x)=x^2-7 (Note: I tried 5 times but I still got this wrong. Plz help)

Calculus
A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show your working, including any derivatives you need...

calculus
find the following derivatives: f(x) = (2x+5)/(x^2-3) f'(x)= (2)*(x^2 -3)-(2x+5)*2x/(x^2-3)^2 is that correct??? f(x)= (lnx)(cos x) f'(x)= 1/x*-sinx or do i have to use the product rule?? thank you.

use the derivatives of y=sinx and y=cosx to develop the derivative of y=tanx

Calculus AB
Evaluate the following derivatives at the given points. Find the equation of the line tangent at each point. a) f(x)=ln(secx) @ x=pi/3 b) f(x)=(root(x+1))/(x-1) @ x=0

calculus
Just doing example questions to better understand. Find all first and second partial derivatives for the function u= xy^2+x^2y

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

calculus
Use Fundemental Theorem of Calculus part 1 to find the derivatives of the following: (i) F(x)=Integral ( top3, bottom x) e^-t^2 dt (ii) G(theta)=Integral ( top cos theta, bottom sin theta) 1/1-x^2 dx

math/ calculus
full work out with explanation of this problem please we're working with derivatives and i don't understand it given h(x)= cotx/x find h'(pi/2)

Calculus
Find the derivatives of the function k(x)=sqrt(sin(2x))^3 I think I have the answer and was wondering if i had it correct k'(x)=2sin(x)^3+8sin(x)

Use L'Hospital's Rule to solve: lim u --> 1 of (u-1)^3/ ((1/u) - u^2 + (3/u) - 3) Ok, so what I thought was that it is type 0/0 so taking the derivatives of the top and bottom 3(u-1)^2 /(-u^-2 -2u - 3u^-3) and subbing in u = 1 = 0/-6 = 0

Calculus - First Derivatives
Find K'. Y = K^(0.25) * L^(0.75).... relates to Cobbs-Douglas function (dL/dK) = 0.25 (K/L)^(0.25) I got to this.... but answer is... (dL/dK) = 0.25 Y/L <--- Please provide a full solution (all steps..) to get to this....

Calculus derivatives
f(a) = a + √a (a) Find the derivative of the function using the definition of derivative.

Calculus
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2 the sqrt is just over t.

calculus derivatives update
update yes, sorry I wrote it wrong (mx)= (x^5-5x^3 +7x-4)^10 * (4x^9 +19)^23 Thanks again

Calculus Partial Derivatives
y=F(x+at) + f(x-at) y=F(w) + f(v) (w=x+at, v=x-at) don't see how to get from here to partial derivative y with respect to t = F"(w)a^2 + f"(v)a^2

Calculus-partial derivatives
Let Z = f(u,v) where u=xy^3 + e^3 and v = (x^2)y. Obtain expressions for Zx and Zy in terms of fu and fv. I don't understand the "in terms of" part. How do I do this question? thank you

Calculus

Calculus
Why are these false? If a function has derivatives from both the right and left at a point then its differentiable at that point.

calculus
How do you estimate derivatives when you don't know the actual equation of the line on the graph, but you have just a picture of the graph?

Calculus Derivatives
Determine the concavity of f(x)=xlnx I end up with F''(x)=1/x, where it would be concave up when x>0 and concave down when x<0 Is this correct?

calculus
Find a function f such that the curve y = f(x) satisfies y'' = 12x, passes through the point (0,1), and has a horizontal tangent there. I can use the anti-derivatives to get y = 2x^3 + Cx + D but I don't know how to get C even though I know D = 1.

Calculus
Hi~ Thank you for your help! I was trying to work on a problem about Taylor series, but i don't think im approaching the problem the right way. I have to find the fifth order Taylor polynomial and Taylor series for the function f(x) at x = 0. f(x) = 1/(x+2) I tried to just ...

calculus
PLEASE HELP Find the first and second derivatives of the function. y = e^8ex. I keep getting y' = e^8ex * 8 and its wrong. how do you do this?

calculus
let f be a function 0 to 2pi with continuous first and second derivatives and suchthat f"x>0 for 0<x<2pi integral f(x)cosx from 2pm to 0

Calculus (Derivatives)
Show the steps to get the derivative function of -500/x by evaluating the limit. By limit, they are referring to the equation, lim h -> 0 (f(x + h)-f(x))/h

Calculus derivatives
Consider the equation x^2 + xy + y^2 = 1 Find all points where the tangent line is parallel to the line y = −x. Thank you for helping

Calculus
Find the partial derivatives of f(x,y)=(sinx + y)^(y sinx)

Calculus
Find the derivatives of the function f(y)= sinh(sinh(7y).

Calculus
a) Find d/dm (x^4m^5 + y^3m +z^6) b) Find the first and second derivatives of: v = 3t^2 + 8t + 11 v' = v'' =

calculus
Quadratic function written in standard form where a, b, and c are constants such that a is not zero. f(x)= ax^2+bx+c Using calculus find the vertex of the parabola formed by this quadratic function. Determine under what conditions this vertex is a maximum or minumum (using ...

Calculus - Derivatives
I need help finding the derivative of 100P^-2 I know that 100P^2 would be 200P, but the -2 is throwing me off. Could someone help me out here? Thanks.

Calculus (derivatives)
Find the points on the graph of f where the tangent line is horizontal. x/x^2+25 I know you have to do the quotient rule to find the derivative, but then I do not know what to do after that.

calculus
let f be the function f(x) = e^(2x^2) find the first four nonzero terms and the general term of the power series for f(x) about x = 0 i tried doing this problem but finding the derivatives gets way too complicated can anyone help??

Calculus Partial Derivatives
Problem: Find dimensions of a box that provide the greatest volume when the length plus the girth cannot exceed six feet. I tried 2w+2h+l=6, l=6-2w-2h, but couldn't get to w=1, h=1, l=2, which is the correct answer.

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