# Calculus - Derivatives

17,265 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 ...

### Calculus grade 12

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

if f(x)=x^3+5x, then f'(2)= if f(x)=cos(2x), then f'(pi/4) derivatives and anti derivatives please help

### 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

Find the derivatives of the following function: i)y=-3x^-3 +2x^-2 + x-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

Find the derivatives of the function f(t)=cosh^2(4t)-sinh^2(4t). Simplify your answer completely.

### 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.

### Calculus Review for exam grade 12, please help.

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)

### Calculus - PLEASE HELP!!

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

Find the first and second derivatives of the given functions. y=¡î(x©÷+1) y'=x(x©÷+1)^(-1/2) y"=[1(x©÷+1)^(-1/2)]-[(1/2)[(x©÷+1)^(-3/2)](2x)(x)] y"=[(x©÷+1)^(-1/2)]-[(x©÷)(x©÷+1)^(-3/2)] Is the second derivative right?

### 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

How many units should this company sell to maximize their revenue if the revenue function was -(x^2/100)+50x using derivatives?

### 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.