Calculus Review Game - Finding Derivatives

Basic Derivative Information and Power Rule

100

Find the derivative of y = 9

y' = 0

200

d/dx 6x³ +5 =

18x²

300

d/dx 3/x =

-3/x² or -3x^-2

400

Differentiate 8/x² - 5/x

-16x^-3 + 5x^-2

Chain Rule

100

d/dx (x²)³

6x(x²)² or 6x⁵

200

d/dx (3x+1)²

6(3x+1) or 18x+6

300

Differentiate 5(2x²+5x)³

15(2x²+5x)²(4x+5) or (60x+75)(2x²+5x)²

400

Differentiate y=(1+sinx)⁴

y'=4(1+sinx)³(cosx)

or y'=4cosx(1+sinx)³

Product Rule

100

Differentiate y=2x⁴(4x-1)

y′ =2x⁴(4)+8x³(4x-1)

8x⁴+32x⁴-8x³

40x⁴-8x³

200

f(x)=(2x+10)(3x-5), what is f′(x)?

(2x+10)(3)+(3x-5)(2) = 12x+20

300

Differentiate y=e^x(4x - 7)

y′ = 4e^x + e^x(4x - 7)

400

Differentiate y=x²sin(x)

y′ =x²cos(x)+2xsin(x)

Quotient Rule

100

Differentiate y= 2/(x+1)

Simplify.

y′ = -2/ (x+1)²

200

f(x)= (2x - 1)/ (4x + 6), what is f′(x)?

Simplify.

f′(x)= 16 / (4x + 6)²

300

Differentiate y= (x² - 5x) / (3x+1)

y′= [(3x + 1)(2x - 5) - 3(x² - 5x)] / (3x+1)²

400

Differentiate and simplify y = sinx / cosx

y′ = [-cos²x-sin²x] / cos²x

Trig and Exponential Derivatives

100

Find dy/dx for y = 2e^x

dy/dx = 2e^x

200

Differentiate y=ln(5x²) and simplify

y′ = 2/x

300

Differentiate y=4e^2x+1

y′ =8e^2x+1

400

d/dx 3cos(2x)

-6sin(2x)