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  • Please solve RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 26 maths textbook solution

Please solve RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 26 maths textbook solution

Answers (1)

Answer:

f^{\prime}(x)  is an odd function.

Hint:

Differentiate equation on the both sides with respect to x.

Given:

f^{}(x)  is an even function.
Solution:  

f^{}(x)  is an even 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 odd function.

 

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