1. Derivative of
Logarithmic Function

2. 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.

3. PROPERTIES OF THE NATURAL LOGARITHM

4. Example 1:
Solution

5. 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

6. Example 3: Differentiate
Solution

7. Example 4: Differentiate
Solution

8. Example 5: Differentiate
Solution

9. Derivative of Logarithmic Function
ASSESSMENT
Derivative of Logarithmic Function

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

11. e: f:

12. Solutions: a: b: c: d:

13. e: f: