Table of Derivatives

This flashcard set covers key derivatives and rules from calculus.

Derivative of exponential function

The derivative of e^x is e^x.

Derivative of natural logarithm function

The derivative of ext{ln}|x| is rac{1}{x}.

Derivative of logarithm function

The derivative of ext{log}_b{x} is rac{1}{x ext{ln}(b)}.

Derivative of hyperbolic sine function

The derivative of ext{sinh}(x) is ext{cosh}(x).

Derivative of hyperbolic cosine function

The derivative of ext{cosh}(x) is ext{sinh}(x).

Derivative of hyperbolic tangent function

The derivative of ext{tanh}(x) is ext{sech}^2(x).

Derivative of cotangent function

The derivative of ext{cot}(x) is - ext{csc}^2(x).

Product Rule

The derivative of the product of two functions, f(x)g(x), is given by f'(x)g(x) + f(x)g'(x).

Quotient Rule

The derivative of the quotient of two functions, rac{f(x)}{g(x)}, is given by rac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}.

Power Rule

The derivative of x^n for real numbers n is nx^{n-1}.