Differentiation of Exponential Functions
Formulas and examples of the derivatives of exponential functions, in calculus, are presented. Several examples, with detailed solutions, involving products, sums and quotients of exponential functions are examined.
First Derivative of Exponential Functions to any BaseThe derivative of f(x) = b^{ x} is given byNote: if f(x) = e^{ x} , then f '(x) = e^{ x} Example 1Find the derivative of f(x) = 2^{ x}Solution to Example 1
Example 2Find the derivative of f(x) = 3^{ x} + 3x^{ 2}Solution to Example 2
Example 3Find the derivative of f(x) = e^{ x} / ( 1 + x )Solution to Example 3
Example 4Find the derivative of f(x) = e^{ 2x + 1}Solution to Example 4
ExercisesFind the derivative of each function.1 - f(x) = e^{ x} 2^{ x} 2 - g(x) = 3^{ x} - 3x^{ 3} 3 - h(x) = e^{ x} / (2x - 3) 4 - j(x) = e^{ (x2 + 2)} Solutions to the Above Exercises1 - f '(x) = e^{ x} 2^{ x} ( ln 2 + 1) 2 - g '(x) = 3^{ x} ln 3 - 9x^{ 2} 3 - h '(x) = e^{ x}(2x -5) / (2x - 3)^{ 2} 4 - j '(x) = 2x e^{ (x2 + 2)} More References and linksdifferentiation and derivativesExponential Functions Tutorial on Exponential Functions (1) |