All Derivatives needed for CLEP Calculus

All the derivatives you must memorize for CLEP Calculus.

Limit Definition of a Derivative

Power Rule

Chain Rule

Product Rule

Quotient Rule

Constant Rule

Constant Rule

Constant Multiple Rule

Sum/Difference Rule

e^x

Derivative of e^x

a^x ln a

Derivative of a^x

1/x

Derivative of ln x

1 / x ln a

Derivative of log base a of x

cos x

Derivative of sin x

-sin x

Derivative of cos x

sec²x

Derivative of tan x

sec x tan x

Derivative of sec x

-csc x tan x

Derivative of csc x

-csc²x

Derivative of cot x

Derivative of sin^-1 x

Derivative of cos^-1 x

Derivative of tan^-1 x

Rolle's Theorem states that if a function is continuous on a closed interval and differentiable on an open interval, and if the function has equal values at the endpoints, then there exists at least one point within the interval where the derivative of the function is zero.

Rolle’s Theorem

f`(x)

First Derivative

f``(x)

Second Derivative

f^n (x)

nth Derivative

L’Hopital’s Rule

Derivative of an inverse function

Formula for average rate of change over an interval