Mathematics

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

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

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.

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

Solution Cont.

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

Example-3

Con.

Con.

Con.

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

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

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

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

Example-5

Con.

Example-6 Solution: Putting x = tanq

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

Second Order Derivatives First order differential coefficient Second order differential coefficient

Example-7 Solution:

Example-8

Con.

Thank you