Derivative of Logarithmic Function

Logarithmic Differentiation The Function y = ( f (x)) g (x) We take the natural logarithm of both sides of the equation y = ( f (x))g(x), to btain  ln y = ln ( f (x))g(x) = g(x) ln f (x) Then we differentiate implicitly both sides of the resulting equation ln y = g(x) ln f (x) with respect to x.

PROPERTIES OF THE NATURAL LOGARITHM

Example 1: Solution

Example 2: Differentiate y = xx Solution Apply the natural logarithm to both sides of this equation getting Differentiate both sides of this equation. Multiply both sides of this equation by y, getting

Example 3: Differentiate Solution

Example 4: Differentiate Solution

Example 5: Differentiate Solution

Derivative of Logarithmic Function ASSESSMENT Derivative of Logarithmic Function

Using logarithmic differentiation, differentiate: b: c: d:

e: f:

Solutions: a: b: c: d:

e: f: