356 Answered Questions for the topic Derivatives

Use linear approximation and differential to approximate : 14^(1/4)

Use linear approximation and differential toto approximate : 14^(1/4)

Use linear approximation and differential to approximate: sin 31`

Use linear approximation and differential to approximate: sin 31`

A particle moves in a straight line from its initial position so that after t seconds, it distance is given by s = t^2 + t feet from its initial position.

(a) Find the average velocity of the particle over the interval [1; 3] seconds.(b) Find the instantaneous velocity of the particle at t = 1 second.
Derivatives

04/17/15

A spherical ballon is inflated so that its volume is increasing at the rate of 20 cubic feet per minute. How fast is the surface area of the ballon increasing

A spherical ballon is inflated so that its volume is increasing at the rate of 20 cubic feetper minute. How fast is the surface area of the ballon increasing when the radius is 4 feet?
Derivatives

04/17/15

d/dx ( sin^2 x y cos x y = 1) 

Find the derivative of the following functions:
Derivatives Calculus

04/02/15

NEED ANSWERED ASAP Find dy/dx when x=2 given that y=³vu and u= x2 +x+1

Find dy when x=2 given that y=³√u and u= x2 +x+1       dx
Derivatives

04/02/15

derivative of f(x)=6e^2x

find the derivative of 6e^2x
Derivatives

03/18/15

where the following graph has a vertical tangent line

4x/(x2+4)

03/15/15

what is the derivative of y=(8cos9x-9cos8x)/(9sin8x-8sin9x) using Product Rule not QR

what is the derivative of y=(8cos9x-9cos8x)/(9sin8x-8sin9x) using Product Rule not QR

03/15/15

find derivative of y=(4x^3 - 12xtan12x - 6cos6x)/(5x^4) using Product Rule not QR please!

find derivative of y=(4x^3 - 12xtan12x - 6cos6x)/(5x^4) using Product Rule not QR please!

03/15/15

find trig derivative of y= (2x-cosx^2-sinx^2-xcosx-xsinx-x^2cosx-x^2sinx-x^2)^4

find trig derivative of y= (2x-cosx^2-sinx^2-xcosx-xsinx-x^2cosx-x^2sinx-x^2)^4   i'm unsure about the cancellations at the end when you reduce to get the final answer, please help!

03/15/15

find trig derivative of y=4x^2 csc^4 4x^2 cot^4 4x^2

find trig derivative of y=4x^2 csc^4 4x^2 cot^4 4x^2   I got y'= 8xcsc^4 4x^2 cot^4 4x^2 - 128x^3 csc^4 4x^2 cot^4 4x^2 - 128x^3 cot^3 4x^2 csc^6 4x^2   I just wasn't sure if i did this... more

03/15/15

Find trig derivative of (4x^5)/(8cot^4 x^3) using PRODUCT RULE not QR

Find trig derivative of (4x^5)/(8cot^4 x^3)I got y'=20x^4(1/8tan^4 x^-3) + -3/2xsec^2 x^-3 but im not sure if it's correct. any help is greatly appreciated!

03/06/15

FUNTIONS f(t) = 2w^3-33w^2+180w+11

The function  f(t) = 2w^3-33w^2+180w+11 has one local minimum and one local max.  This function has a local minimum at x = ? with the value ? and a local maximum at x equals ? with value ?

03/04/15

R (t) = 0.00731t^4 – 0.174t^3 + 1.528t^2 + 0.48t + 19.3; (0=t=10)

The share of the world population that is over 60 years of age compared to the rest of the working population in the world is of concern to economists. An increasing dependency ration means that... more
Derivatives Calculus

03/04/15

F(x)=1/3 t^3-5/2 t^2+80;(0=t =10) Find the intervals where the function F(t) is increasing and the intervals where it is decreasing.

The Department of Environment and Natural Resources began to record an index of environment quality that measured progress and decline in the environmental quality of its forests. The index for the... more
Derivatives

02/26/15

Find the derivative: lim x-->0 (sin3x)/(5x^3-4x)

I'm pretty lost on how to begin this problem. 

02/26/15

A water trough is 6 m long and its cross-section is an isosceles triangle which is 60 cm wide at the top, and the height is 30 cm.

A water trough is 6 m long and its cross-section is an isosceles triangle which is 60 cm wide at the top, and the height is 30 cm. The trough is not full. Give an expression for V, the volume of... more
Derivatives

02/26/15

What's the derivative of tsint/1+t? With steps please! I'm having trouble with simplification.

Here's what I have:   f(x)= tsint/1+t f1(x)= (1+t)(tcost+sint)-(tsint)(1)/(1+t)2 f1(x)= tcost+sint+t2cost+tsint-tsint/(1+t)2   After this my answers keep coming out incorrect in comparison to... more
Derivatives

02/25/15

Calculate the derivatives of the following functions

4x2e5x   (t2+tan t)3   √x+2 cos3 x / 2x-5   sec(tan x)   (√x+(√x))   ln(3x2+5)   5lnx   xsin-1 (1-x2)

02/21/15

linear approximation and derivative help

A right circular cone of height h and base radius r has total surface area S consisting of its base area plus its side area, leading to the formula: S= pi*r^2+pi*r*sqrt(r^2+h^2)Suppose you start... more
Derivatives

02/19/15

cos(x+y)=pi+x^2y

Find dy/dx for the function:
Derivatives Calculus Limits

02/19/15

Given that f'(x)=lnx evaluate the limit as h approaches 0 (f(2+h)-f(2))/h

Please explain how to do this 
Derivatives Calculus

02/19/15

derivative of x^cosx

i tried using ax(lna) and got xcosx(lnx) but I'm not sure if that's right or if I'm even done yet.
Derivatives Differentiation Ib

02/19/15

Writing equations for lines...

Write an equation for the line tangent to the curve f(x) = 4ex - 7 at x = ln 3   Could someone please explain how I might go about answering this question? Thank you!

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