1. Mathematics

2. Session Differentiation - 2

3. Session Objectives  Fundamental Rules, Product Rule and Quotient Rule  Differentiation of Function of a Function  Differentiation by Trigonometric Substitutions  Differentiation of Implicit Functions  Class Exercise

4. Fundamental Rules

5. Example-1 Differentiate the following:

6. Solution Differentiating y with respect to x, we get

7. Product Rule Ifand are differentiable functions, then

8. Example-2 Differentiating w.r.t. x, we get Differentiate: w.r.t. x. Solution Let y =x 2 sinxlogx

9. Quotient Rule Ifand are differentiable functions and, then

10. Example-3 Differentiate: w.r.t. x. Solution: Differentiating w.r.t. x, we get

11. Differentiation of Function of a Function Note: If and, then If ƒ(x) and g(x) are differentiable functions, then ƒog is also differentiable (Chain Rule)

12. Example-4 Differentiatew. r. t. x. Solution: Differentiating y w.r.t. x, we get

13. Example-5

14. Continued

15. Trigonometric Substitutions

16. Example-6 Putting x 2 = cos2 Solution:

17. Continued Differentiating y w.r.t. x, we get

18. Example-7

19. Continued

20. Differentiation of Implicit Functions y is not expressible directly in terms of x

21. Example-8 We have xy 3 – yx 3 = x Solution:

22. Solution Cont.

23. Thank you