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
\[ y = \dfrac{ \tan x }{ e^{ x } } \]

Solution to Example 5



Example 6

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

Solution to Example 6


Example 7

Use the method of taking the logarithms to find \( y' \) if \( y = uv \), 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 \( y = \dfrac{u}{v} \), where \( u \) and \( v \) are functions of \( x \).

Solution to Example 8

More References and links

differentiation and derivatives