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Derivatives

100

The derivative of sin(x)

cos(x)

200

d/dx [x^3 + 2x]

3x^2+2

300

d/dx[(3x^2+2x)^4]

4(3x^2+2x)^3 * (6x+2)

400

Implicit differentiation of xy=5

xdy/dx+y=0

Integrals

100

∫1/x

ln(x)

200

∫3x^2

x^3

300

∫e^(2x)

1/2e^(2x)

400

∫sec^2(x)dx

tan(x) + C

Theorems

100

This theorem guarantees a point where f'(c) = average rate of change

Mean Value Theorem

200

This theorem connects integration and differentiation

FTC

300

This part of this theorem is used to find the value of f(c) given f(0) and f'(x)

FTC Part II

400

Rolle's Theorem requires these 3 conditions

continuous, differentiable, and f(a)=f(b)

Graphs

100

A graph is concave up when this is true

When f''(x) is positive OR when f'(x) is increasing

200

This happens where the second derivative is 0 and changes sign 

Inflection value OR the graph changes concavity 

300

This function has vertical asymptotes at x = π/2 and at x = -π/2

arctan(x)

400

Dont do this one

NANANAN

Potent Puns

100

What do you call an integral that's late

An improper integral

200

Why did the function break up with is derivative

There was a discontinuity

300

What do you call a derivative that went rogue

derivrogue

400

Why was the integral at therapy

it was derived