## Differentiation of Exponential and Logarithmic Functions

Exponential functions and their corresponding inverse functions, called *logarithmic functions,* have the following differentiation formulas:

Note that the exponential function *f*( *x*) = *e* ^{x} has the special property that its derivative is the function itself, *f*′( *x*) = *e* ^{x} = *f*( *x*).

**Example 1:** Find *f*′( *x*) if

**Example 2:** Find *y*′ if .

**Example 3:** Find *f′*( *x*) if *f*( *x*) = 1n(sin *x*).

**Example 4:** Find if *y*=log _{10}(4 *x* ^{2} − 3 *x* −5).