Definition:Logarithmic Differentiation

Definition

Logarithmic differentiation is the technique of obtaining the derivative of an arithmetic expression by obtaining its (natural) logarithm before differentiation.

Examples

Example: $y = 2^x$

Let $y = 2^x$.

Then:

$\dfrac {\d y} {\d x} = 2^x \ln x$

Continued Product

Let $y = x \paren {1 + 2 x} \paren {1 + 3 x}$.

Then:

$\dfrac {\d y} {\d x} = \paren {1 + 2 x} \paren {1 + 3 x} + 2 x \paren {1 + 3 x} + 3 x \paren {1 + 2 x}$

Also see

• Results about logarithmic differentiation can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logarithmic differentiation