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.
The derivative of f(x) = log_{ b} x is given by
Note: if f(x) = ln x , then f '(x) = 1 / x Example 1: Find the derivative of f(x) = log_{ 3} x Solution to Example 1:
Example 2: Find the derivative of f(x) = ln x + 6x^{ 2} Solution to Example 2:
Example 3: Find the derivative of f(x) = log_{ 3} x / ( 1 - x ) Solution to Example 3:
Example 4: Find the derivative of f(x) = ln (-4x + 1) Solution to Example 4:
Exercises Find 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 exercises 1) f '(x) = 2 / x 2) 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 on differentiation and derivatives |