AP Calc. Unit 2 Chain Rule

power rule purpose

helps find derivative of a function quickly

power RULE

if a variable exists

• move exponent to the front as a coefficent

• subtract 1 from the original exponent

if no variable exists

• 0 is the derivative

in general . . .

if f(x) = g(x) ± h(x) then f’(x) = g’(x) ± h’(x)

root . . .

take out root and write as an exponent

• coefficent in numerator and degree in denominator

equation of tangent line at x = a

y-f(a) = m (x-a)

need to have

• slope

• point

• equation

any number’s derivative is always

0

e to the power of x has the derivative of

the same exact thing as the original

x as exponent has the derivative of

the original times ln of the coefficent

ln x has the derivative of

1/x

log base a of x has the derivative

move x to coefficent times ln times coefficent

sin x derivative

cos x

cos x derivative

-sin x