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 |