Differential Calculus :D

CPQ Rule

100

Find f'(x) when f(x)=x^(-1/2)

What is f'(x)= -0.5(x^-1.5)

200

Find f'(x) when f(x)=(2x^4-3x^3+1)/(x^2) 

What is f'(x)=4x-3-2x^-3

300

Find f'(x) when f(x)=(x^3+2x)^10

What is f'(x)=10(x^3+2x)^9(3x^2+2)

400

Find f'(x) when f(x)=(2-3x)sqrt(x+2)

what is f'(x)=(-10-9x)/2sqrt(x+2)

500

Find f'(x) when f(x)=(3-x)^2(sqrt(x+1))

WHat is f'(x)=[(x-3)(5x+1)]/2sqrt(x+1)

Trig Derivatives

100

Find the derivative of cos^2(x)

What is -2sinxcosx or -sin2x

200

Find y' when y=cos(sinx)

What is y'=-sin(sinx)cosx

300

Differentiate y=sin(sqrt(x^2+1))

What is y'=xcos(sqrt(x^2+1))/sqrt(x^2+1)

400

Differentiate y=-cos^4(sinx)

What is y=-4cos^3(sinx)sin(sinx)cosx

500

TEAM MISSION DAILY DOUBLE

Find y' when y=sin[(x^3-1)^4]

What is y'=12x^2(x^3-1)cos[(x^3-1)^4]

Second Derivatives

100

Find the second derivative of function y=4x^3+4x

What is y''=24x

200

What is the second derivatie of the functiopn y=1/(1-x)

What is y''=2(1-x)^-3

300

Find the second derivative of the function y=1/2x-1

What is y''=8(2x-1)^-3

400

DOUBLE DOUBLE DOUBLE DOUBLE TEAM DOUBLE

Given that y=(1-ax)^2 and y''=8, find the value of a when a>0

What is a=2

500

Find 2nd deriv of y=(2x-2)(x^2-2x)^5

What is y''=12(x^2-2x)^4(11x^2-22x+10)

Exponential/Log Derivatives

100

Find the derivative of the function y=e^x

What is e^x

200

Find the derivative of function y=(lnx)^3

What is y'3(lnx)^2/x

300

Find deriv. when y=e^(xlnx)

What is y'=(lnx+1)e^xlnx

400

Find deriv when y=e^(xsinx)

What is y'=e^(xsinx)(sinx+xcosx)

500

Find the derivative of the following function y=ln(ln(sinx))

*HINT WORK FROM OUTSIDE TO INSIDE

What is cos(x)/sin(x)ln(sin(x))

Application

100

When T(n)=18+12ne^(-n/3). Find the average rate of change during the first 18 days of the month

What is 0.0297

200

A particle movesin a horizontal line so that its position from a fixed point after t seconds, where t greater and equal to 0 , is s meters, where 

s(t)-5t^2-t^4. Find the velocity of the particle after 1 second. 

What is 6ms^-1

300

A TRIPLE

F(x)=2x^4-4x^2+1. Find all turning points. 

What is x=0,-1,1

400

Find and classify all points of inflection of f(x)=3x^4+4x^3-2

What is x=0, -0.666666666...

500

A particle moves in a straight line such that its position in metres from a fixed origin is given by s(t)=t^3-3t+1, where ti sthe time in seconds, t greater and equal to 0. 

At what time(s) does the particle reverse direction? 

What is t=1