Derivative rules

Power rule

Multiple exponent by leading term and then subtract one from the orginal exponent

sin x

Cos x

cos x

-sin x

tan x

sec² x

a^x

a^x ln a

e^x

e^x

Log b 

1/ x ln b

ln x

1/x

e

0 - because e is constant so its just 0

Pie²

0 - cuz its constant

X

1

F(x)

F’(x)

Y

dy / dx

Average Rate of Change

Slope - so f(b) - f(a) / b - a

Instantaneous rate of change

derivitiev - point slope form - find point and find slope - y- y1 = m (x-x1)

Limit definition of diveritive 

Lim h→ 0 f(x+h) - f(x) / h

Differentiablity

First continous then differnetiablioty - pick the one with the underline under the greater than or less than sign

1. Find point

2. Find lim

3. Find if lim matches the point

4. Find if the lim of the derivatives match

Differntiablity with multiple variables

Find equations for regular f(x) and f’(x) - set those equal to each other than once you have the two equations use a system of equations to find what either a or b equals

Point 

X,f(x)

Slope

f’(x)

Graphical connections

The slope of the orginal graph is used to find out what the second graph is, such as negative slope then postive woudl make the second graph start under 0 and be negative then go past 0 and become postive 

Product Rule

f(x) . g’(x) + g(x) . f’(x)

Quotient Rule

f’(x) . g(x) - g’(x) . f(x) / g(x)²