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=log₁₀(4 x² − 3 x −5).

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