Product and Quotient Rules Review

Product Rule

100

Find the derivative of y=3x²(7x+2)

y'=63x²+12x

200

Find the derivative of f(x)=(x³-x²)ln(8x)

f'(x)= x²-x+3x²ln(8x)-2ln(8x)

300

**Double Jeopardy**

Find the derivative of y=e^{x^3}x⁷

y'=x⁶e^{x^3}(7+3x³)

400

Find the derivative of f(x)=3^5x(cosx)

f'(x)=3^5x(cosx) * ln3 * [-5(xsinx-cosx)]

500

Find the derivative of y=(x+1)(x-3)

y'=2(x-1)

Quotient Rule

100

Find the derivative f(x)=x⁵/e^x

f'(x)=x⁴(5-x)/e^x

200

Find the derivative y=(x+1)/(x-3)

y'=-4/(x-3)²

300

Find the derivative of f(x)=cos (5/x)

f'(x)=(5/x²) sin (5/x)

or

f'(x)= [5 sin (5/x)]/x²

400

Find the derivative of y=1/(5x+1)

y'=-5/(5x+1)²

500

**Double Jeopardy*

Find the derivative of f(x)=ln[(x+2)/(x-2)]

f'(x)=-4/[(x-2)(x+2)] 

or

f'(x)=-4/(x²-4)

Random

100

**Double Jeopardy**

Find the derivative of y=3x²

y'=6x

200

Find the derivative of f(x)=4^3X

f'(x)=4^3x * ln4 * 3

300

Find the derivative of y=1/x⁴

y'=-4/x⁵

400

Find the derivative of f(x)=log₄(8x)

f'(x)=1/xln4

500

Find the derivative of y=e^x+3

y'=e^x