AP Calc Derivatives and Identities to Know

Memorize the rules we have for derivatives and identities that can be useful.

Product Rule for f(x)=g(x)*h(x)

f’(x)=g’(x)h(x) + g(x)h’(x)

Quotient Rule for f(x) = g(x) / h(x)

f’(x) = ( h(x)g’(x) - h(x)g’(x) ) / (h(x))²

Derivative of a Constant, f(x)=C

f’(x)=0

Derivative of a sum/difference: f(x) = g(x)+h(x)

f’(x) = g’(x) + h’(x)

derivative of cosx

-sinx

derivative of sinx

cosx

derivative of e^x

e^x

derivative of ln(x)

1/x

Power Rule f(x)=x^n

f’(x)=n * x^n-1

Definition of a Derivative

lim as h→0, (f(x+h) - f(x)) / h

Chain Rule

for composite functions (functions inside functions)

derivative of tanx

sec²x

derivative of cotx

-csc²x

d\dx of cscx

-csc(x)cot(x)

d/dx of sec(x)

sec(x)tan(x)

sin²x+cos²x=?

sin²x+cos²x=1

sin(2x) = ?

2sinxcosx

cos(2x)=?

cos²x-sin²x = 2cos²x-1 = 1-2sin²x

sin²x= ?

(1-cos(2x))/2

cos²x = ?

(1+cos(2x)) / 2