Differentiation of Logarithmic Functions
Examples of the derivatives of logarithmic functions, in calculus, are presented. Several examples, with detailed solutions, involving products, sums and quotients of exponential functions are examined.
First Derivative of a Logarithmic Function to any BaseThe first derivative of f(x) = log_{ b} x is given byNote: if f(x) = ln x , then f '(x) = 1 / x ExamplesExample 1Find the derivative of f(x) = log_{ 3} xSolution to Example 1:
Example 2Find the derivative of f(x) = ln x + 6x^{ 2}Solution to Example 2:
Example 3Find the derivative of f(x) = log_{ 3} x / ( 1 - x )Solution to Example 3:
Example 4Find the derivative of f(x) = ln (-4x + 1)Solution to Example 4:
ExercisesFind the derivative of each function.1) f(x) = ln(x^{ 2}) 2) g(x) = ln x - x^{ 7} 3) h(x) = ln x / (2x - 3) 4) j(x) = ln (x + 3) ln (x - 1) Solutions to the Above Exercises1) f '(x) = 2 / x2) g '(x) = 1 / x -7x^{ 6} 3) h '(x) = (2x - 3 - 2x ln x) / [ x(2x -3)^{ 2} ] 4) j '(x) = ln (x + 3) / (x - 1) + ln (x - 1) / (x + 3) More References and linksdifferentiation and derivatives |