Logarithmic Differentiation Method

The method of logarithmic differentiation , calculus, uses the properties of logarithmic functions to differentiate complicated functions and functions where the usual formulas of Differentiation do not apply. Several examples with detailed solutions are presented.

Example 1

y = x sin x

Solution to Example 1



Example 2

Find the derivative y ' of function y defined by
y = x e (-x 2)

Solution to Example 2


Example 3

Find the derivative y ' of function y given by
y = 3 x 2 e -x

Solution to Example 3



Example 4

Find the derivative y ' of function y given by
y = (1 - x) 2 (x + 1) 4

Solution to Example 4


Example 5

Find the derivative y' of function y defined by
y = tan x / e x

Solution to Example 5



Example 6

Find the derivative y' of function y given by
y = [ (x - 2)(x + 4) ] / [ (x + 1)(x + 5) ]

Solution to Example 6


Example 7

Use the method of taking the logarithms to find y ' if y = u v, where u and v are functions of x.

Solution to Example 7



Example 8

Use the method of taking the logarithms to find y ' if y = u / v, where u and v are functions of x.

Solution to Example 8


More References and links

differentiation and derivatives