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  • Please solve RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 1 maths textbook solution

Please solve RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 1 maths textbook solution

Answers (1)

Answer:

The answer will be \frac{1}{e}

Hint:

If f(x)=\log _{e}\left(\log _{e} x\right) then write the value of f^{\prime}(e)

Given: 

\frac{d}{d x} \log _{e} x=\frac{1}{x}

Solution: 

\begin{aligned} &f(x)=\log _{e}\left(\log _{e} x\right) \\\\ &f^{\prime}(x)=\frac{d}{d x}\left[\log _{e}\left(\log _{e} x\right)\right] \end{aligned}

           =\frac{1}{\log _{e} x} \cdot \frac{d}{d x} \log _{e} x

\begin{aligned} &f^{\prime}(x)=\frac{1}{\log _{e} x}\times \frac{1}{x} \\\\ &f^{\prime}(e)=\frac{1}{\log _{e} e}\times \frac{1}{e} \\\\ &f^{\prime}(e)=\frac{1}{e} \end{aligned}

So, the answer will be \frac{1}{e}

 

Posted by

infoexpert26

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