Calculus Review Game- Finding Derivatives

Basic Derivative Information and Power Rule

100

The derivative calculates the ________.

Slope

200

d/dx 5 =

0

300

d/dx x² =

2x

400

d/dx 3x²-x+3 =

6x-1

500

f(x)= 5x⁴+4x³+6x+10

20x³+12x²+6

Chain Rule

100

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

g′(x)f′(g(x))

200

d/dx (3x+1)²

6(3x+1)

300

d/dx sin(4x²)

8xcos(4x²)

400

Differentiate y=√13x²-5x+8

y′ =26x-5/ 2√13x²-5x+8

500

Differentiate y=3tan√x

y′ =3sec²√(x)/ 2√x

Product Rule

100

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

f′(x)g(x)+ g′(x)f(x)

200

f(x)=x²sinx, what is f′(x)?

2xsinx+ x²cosx

300

Differentiate y=x³lnx

y′ =x²(1+3lnx)

400

Differentiate y=e^-x²cos2x

y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x

500

Differentiate y=x²sin³(5x)

y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]

Quotient Rule

100

Define the Quotient Rule using f(x)/g(x)

[g(x)f′(x) - f(x)g′(x)]/ (g(x))²

200

Differentiate y= 2/(x+1)

y′ = -2/ (x+1)²

300

Differentiate y= 5x²/(x+1)

y′=5x²+10/(x+1)²

400

f(x)= 4x/x⁵, what is f′(x)?

f′(x)= -16x5/x¹⁰

500

Differentiate y= 6x(x^-3)

y′ = -12x3/x⁶

Trig Derivatives

100

d/dx cosx=

-sinx

200

Differentiate y=tan(x)

y′ =sec²(x)

300

Differentiate y=csc(x)

y′ =-csc(x)cot(x)

400

d/dx sin(2x)

2cos(2x)

500

d/dx cot(2x)

-2csc(2x)