Calculus Review Game

Power Rule

100

Find f'(x) for:  f(x)=axⁿ

(basic formula)

f'(x)=a*n*x^n-1

200

Find f'(x) for:

f(x)= 5x⁸-3x²+2x

f'(x)= 40x⁷-6x+2

300

Find f'(x) for:

f(x)= 10x³+5x²+8x+16

f'(x)= 30x²+10x+8

400

Find f'(x) for:

f(x)= f(x)=x^1/2

f'(x)= 1/(2x^1/2)

500

Find f'(x) for:

f(x)=2x^2/3-4x^9/4

f'(x)= 4/(3x³)-9x^5/4

Product Rule

100

Find: d/dx [f(x)*g(x)]

(basic formula)

=f(x)*g'(x)+ g(x)*f'(x)

200

Find dy/dx for:

y= (x²+1) (x³+x+5)

dy/dx= 5x⁴+6x²+10x+1

300

Find dy/dx for:

y= (x²+3) (x²-4x)

dy/dx= 4x³-12x²+6x-12

400

Find dy/dx for:

y= (2x³+6) (x⁴+3x)

dy/dx= 14x⁶+48x³+18

500

Find dy/dx for:

y= (7x²+10) (x²+2x)

dy/dx= 28x³+42x²+20x+20

Quotient Rule

100

Find: d/dx [f(x)/g(x)]

(basic formula)

=[g(x)*f'(x) - f(x)*g'(x)] / [g(x)]²

200

Find dy/dx for:

y= (x²+1) / (3x-2)

dy/dx= (3x²-4x-3) / (3x-2)²

300

Find dy/dx for:

y= (3x-1) / (x³+6)

dy/dx= -(6x³-18-3x²) / (x³+6)²

400

Find dy/dx for:

y= (4-3x-x²) / (x²-1)

dy/dx= (3x²-6x+3) / (x²-1)²

500

Find dy/dx for:

y= (4x³+1) / (x²+6)

dy/dx= (4x⁴+72x²-2x) / (x²+6)²

Chain Rule

100

Find y' for:  y= f(g(x))

(basic formula)

y'= f'(g(x))* g'(x)

200

Find y' for: 

y= (4x+12)²

y'= 32x+96

300

Find y' for:

y= (9x+6)²

y'= 162x+108

400

Find y' for:

y= (6x²+1)⁴

y'= 48x(6x²+1)³

500

Find y' for:

y= (2x⁴+7)²

y'= 32x⁷+112x³

Mixed

100

What rule would you use to solve the following:

f(x)= 9x²

Power Rule

200

What rule would you use to solve the following:

f(x)= 2x³+6x²+28x

Power Rule

300

What rule would you use to solve the following:

f(x)= (9x+7) (x²+15)

Product Rule

400

What rule would you use to solve the following:

f(x)= (x-12) / (2x³+5)

Quotient Rule

500

What rule would you use to solve the following:

y= (6x+2)⁷

Chain Rule