Calculus Review Game- Finding Derivatives

Basic Derivative Information and Power Rule

100

d/dx 5 =

0

200

d/dx x² =

2x

300

d/dx 3x²-x+3 =

6x-1

400

The derivative calculates the ________.

Slope

500

Another word for slope is_____________

Tangent

Chain Rule

100

d/dx (3x+1)²

6(3x+1)

200

d/dx sin(4x²)

8xcos(4x²)

300

Differentiate y=(13x²-5x+8)^1/2

y′ =26x-5/ 2√13x²-5x+8

400

Define the Chain Rule for f(g(x))

g′(x)f′(g(x))

500

Differentiate y=3 sin √x

y′ = (3 cos √x)/(2√x)

Product Rule

100

f(x)=x²sinx, what is f′(x)?

2xsinx+ x²cosx

200

Differentiate y=x³lnx

y′ =x²(1+3lnx)

300

Differentiate y=e^-x²cos2x

y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x

400

Define the Product Rule using f(x)g(x)

f′(x)g(x)+ g′(x)f(x)

500

Differentiate y=x²sin(x)

y′ =x²cosx + 2x sinx 

Chain Rule 2

100

Differentiate y= 2(x+1)⁴

y′ = 8(x+1)³

200

Differentiate y= x+ln(3x²)

y′= 1+(6x)/(3x²)=1+2/x

300

f(x)= cos (x²-1)

f′(x)= - 2x sin (x²-1)

400

Derivate: y=e^4x+2 + Sin 3x⁵

y= 4e^4x+2+ 15x⁴cos 3x⁵

500

Differentiate y= 4/(2x-1)⁴

y′ = -32/(2x-1)⁵

Special Derivatives

100

Differentiate y=e^x

y′ = e^x

200

Differentiate y=sin x

y′ = cos x

300

d/dx= cosx

-sin x

400

d/dx cosx=

-sinx

500

d/dx=sin x + cos x + e^x - ln x 

cos x - sin x +e^x - 1/x