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).