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  • Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 27

Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 27

Answers (1)

Answer:

f^{\prime}(x)  is an even function
Hint:

Differentiate equation on the both sides with respect to x.

Given:

f(x) is an odd function.
Solution:  

f(x) is an odd function.

This means that f(-x)=-f(x)

If we differentiate this equation on both sides with respect to x, we get.

\begin{aligned} &f^{\prime}(-x) \cdot(-1)=-f^{\prime}(x) \\\\ &\text { or, } f^{\prime}(-x)=f^{\prime}(x) \end{aligned}

i.e,f^{\prime}(x)  is an even function

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