1. Mathematics

2. Differentiation - 3 Session
I am going to take a session in mathematics , the topic is
Linear equation in two variables.

3. Session Objectives Logarithmic Differentiation, Infinite Series
Differentiation of Parametric Functions, Functions w. r. t. Another Function
Second Order Derivatives
Class Exercise

4. Logarithmic Differentiation
(1) When the functions of the form
we first take logarithms and then differentiate.
(2) When the function is a product of many simpler functions.
Sin2x Sin3x Sin4x
In this case, logarithm converts the product into a sum.

5. Taking log of both sides, we get
Example-1
Differentiate: w.r.t. x.
Solution:
Taking log of both sides, we get
Taking log again, we get

6. Solution Cont.

7. Taking log of both sides, we get
Example-2
Differentiate: Sin2x Sin3x sin4x w.r.t.x.
Solution:
Let y = Sin2x Sin3x sin4x
Taking log of both sides, we get

8. Example-3

9. Con.

10. Con.

11. Con.

12. Differentiation of Infinite Series
Taking log on both sides, we get
logy = ylogx

13. When two variables x and y are expressed in the form
Parametric Functions
When two variables x and y are expressed in the form
x = f(t), y = g(t) , where t is a parameter

14. Differentiating w.r.t. t, we get
Example-4
Solution:
We have x = acos3t and y = asin3t
Differentiating w.r.t. t, we get

15. Differentiation of Functions w. r. t. Another Function
u = f(x) and v = g(x)
Derivative of f(x) with respect to g(x) is

16. Example-5

17. Con.

18. Example-6
Solution:
Putting x = tanq

19. Differentiating w.r.t. x, we get
Solution Cont.
Differentiating w.r.t. x, we get

20. Second Order Derivatives
First order differential coefficient
Second order differential coefficient

21. Example-7
Solution:

22. Example-8

23. Con.

24. Thank you