Calculus Review Game- Finding Derivatives

Power Rule and Tangent Points

100

The derivative calculates the ________.

Slope

200

Find the slope of the graph of the function at the given point.

f(x)=2x⁴-8 at x=1

f'(1)=8

300

Write the equation of the tangent line.

f(x)=3x²-4x  at x=1

y+1=2(x-1)

400

Find the equation of the normal line.

f(x)=8x^-2+3x²  at x=-2

y-14=1/10(x+2)

500

Find the equation of the tangent line.

f(x)=3cos x - 2x at x=0

y-3=-5(x-0)

Negative Exponents

100

d/dx 1/x

-1/x²

200

d/dx 2/3x³

y'=-2/x⁴

300

d/dx 1/x^1/2

y'=-1/2x^3/2

400

d/dx x^1/2-x^-1/2

y'=1/2x^1/2+1/2x^3/2

500

Differentiate y=14x^2/7

y′ = 4/x^5/7

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+3x²lnx

400

Differentiate y=2x²cos(x)

y'=4xcos(x)-2x²sin(x)

500

Differentiate and simplify

 y=(4x²-3)(2x³-1)

y′ =40x⁴-18x³-8x

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

Find the derivative

y=sin (x)/x⁴

y'=[x⁴cos(x)-4x³sin(x)]/x⁸

400

f(x)= (x²-1)/ (x²+1), what is f′(x)?

f'(x)=4x/(x²+1)²

500

If velocity is v(t), find the acceleration, a(1)

v(t)=90t/(4t+10)

a(1)=225/49

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 sec (x)

y'=sec(x)tan(x)

500

d/dx -cot(x)

y'= csc²(x)