Calculus Review Game- Finding Derivatives

Basic Derivative Information and Power Rule

100

The derivative calculates the ________.

Slope of the tangent line

200

d/dx (5) =

0

300

d/dx (x²) =

2x

400

d/dx (3x²-x+3) =

6x-1

500

d/dx (15x^1/3-12x^3/4)

5x^-2/3 - 9x^-1/4

Chain Rule

100

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

f′(g(x))*g′(x)

200

d/dx [(3x+1)²]

6(3x+1)

300

d/dx [sin(4x²)]

8xcos(4x²)

400

Differentiate y=(13x²-5x+8)^1/2

y′ =1/2(26x-5)(13x²-5x+8)^-1/2

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 and factor: y=x³lnx 

y′ =x²(1+3lnx)

400

Differentiate and factor: y=e^-x²cos2x 

y′ =−2e^(−x²) [xcos2x+sin2x]

500

Differentiate and factor: y=x²sin³(5x)

y′ =xsin²(5x)*[15xcos(5x)+2sin(5x)]

Quotient Rule

100

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

[f′(x)g(x) - f(x)g′(x)]/ [g(x)]²

200

Differentiate (no negative exponents): y= 2/(x+1)

y′ = -2/(x+1)²

300

Differentiate & simplify numerator: y= (1+lnx)/(x²-lnx)

y′= (1/x-x-2xlnx)/(x²-lnx)²

400

Find f′(x) and factor: f(x)= (x²-1)³/(x²+1)

f′(x)= [4x(x²-1)²(x²+2)]/[(x²+1)²]

500

Differentiate y= (x³lnx)/(x+2)

y'=[(3x²lnx+x²)(x+2)-x³lnx]/(x+2)²

y′ = [x²(2xlnx+6lnx+x+2)]/(x+2)²

Trig Derivatives

100

d/dx (cosx)=

-sinx

200

Differentiate y=tan(2x)

y′=2sec²(2x)

300

Differentiate y=csc(x²)

y′ =-2xcsc(x²)cot(x²)

400

d/dx [sin(e^x)]

e^xcos(e^x)

500

d/dx [cos⁴x/(1-sin²x)]=

-2cosxsinx