Derivatives of Logarithmic Functions

John Napier (1550–1617), the inventor of logarithms

Pg.244 deriving formulas from

definition

Pg.244 deriving formulas from

definition

Example: Find the derivative.

3ln 2 xxf

Example: Find the derivative.

1

ln

x

xxf

One more example !!!

Find the derivative of

Lets try this again

Find the derivative of

therefore

so…

Logarithmic Differentiation

The derivative of is to messy to calculate directly

so we first take the natural logarithm of both sides and use its properties.

therefore