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

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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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