Rule 1: Differentiation is linear
a and b are real numbers.
h'(x)=af'(x)+bg'(x)

Special cases:
Constant factor rule
(af)'=af'
Sum rule:
(f+g)'=f'+g'
Subtraction rule
(f-g)'=f'-g'

Product rule:
h'(x)=(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)

Chain rule:
h'(x)=(f(g(x)))'=f'(g(x))*g'(x)

Inverse function rule
g(f(x))=x and f(g(y))=y then g'=1/(f'og)

(ln(x))'=1/x if x>0
(x^x)'=(x^x)(1+ln(x))