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Mathematics
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Differentiation - 3 Session
I am going to take a session in mathematics , the topic is Linear equation in two variables.
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Session Objectives Logarithmic Differentiation, Infinite Series
Differentiation of Parametric Functions, Functions w. r. t. Another Function Second Order Derivatives Class Exercise
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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.
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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
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Solution Cont.
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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
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Example-3
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Con.
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Con.
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Con.
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Differentiation of Infinite Series
Taking log on both sides, we get logy = ylogx
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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
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Differentiating w.r.t. t, we get
Example-4 Solution: We have x = acos3t and y = asin3t Differentiating w.r.t. t, we get
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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
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Example-5
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Con.
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Example-6 Solution: Putting x = tanq
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Differentiating w.r.t. x, we get
Solution Cont. Differentiating w.r.t. x, we get
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Second Order Derivatives
First order differential coefficient Second order differential coefficient
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Example-7 Solution:
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Example-8
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Con.
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Thank you
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