 StatLect

# Derivatives - Review

This review page contains a summary of differentiation rules, that is, of rules for computing the derivative of a function. If is a function, its first derivative is denoted by . ## Derivative of a constant function

If is a constant function where , then its first derivative is ## Derivative of a power function

If is a power function then its first derivative is where is a constant.

## Derivative of a logarithmic function

If is the natural logarithm of , that is, then its first derivative is If is the logarithm to base of , that is, then its first derivative is (remember that ).

## Derivative of an exponential function

If is the exponential function then its first derivative is If the exponential function does not have the natural base , but another positive base , that is, if then its first derivative is (remember that ).

## Derivative of a linear combination of functions

If and are two functions and are two constants, then In other words, the derivative of a linear combination is equal to the linear combinations of the derivatives. This property is called "linearity of the derivative".

Two special cases of this rule are ## Derivative of a product of functions

If and are two functions, then the derivative of their product is ## Derivative of a composition of functions (chain rule)

If and are two functions, then the derivative of their composition is What does this chain rule mean in practice? It means that first you need to compute the derivative of : Then, you substitute with : Finally, you multiply it by the derivative of : ## Derivatives of trigonometric functions

The trigonometric functions have the following derivatives: while the inverse trigonometric functions have the following derivatives: ## Derivative of an inverse function

If is a function with derivative then its inverse has derivative The book

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