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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) = ex has the special property that its derivative is the function itself, f′( x) = ex = 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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