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

Speed is _________.

the absolute value of velocity

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=x³(x+1)

y′ =4x³+3x²

400

Differentiate y=-x²cosx

y′ =x²sinx-2xcosx

500

Differentiate y=x²sinx-2x³cosx

y′ =2xsinx+x²cosx-6x²cosx+2x³sinx

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= (1+x) / (x²-x)

y′= (-x²-2x+1)/(x²-x)²

400

f(x)= (x²-1)²/ x²+1, what is f′(x)?

f′(x)=(2x⁵+4x³-6x)/(x²+1)²

500

Differentiate y= (x³sinx)/(x+2)

y′ = [x²(2xsinx+6sinx+x²cosx+2xcosx)]/(x+2)²

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 secx

secxtanx

500

d/dx cotx/cscx

-csc²x-cot²x/cscx