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  • Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 3

Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 3

Answers (1)

Answer:

The answer of the following will be  \frac{2}{e}

Given:

\text { If}f^{\prime}(1)=2 \text { and } y=f\left(\log _{e} x\right), \text { find } \frac{d y}{d x} \text { at } x=e

Hint:

\frac{d y}{d x}=\frac{d}{d x}\left[f\left(\log _{e} x\right)\right]

Solution:  

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

\begin{aligned} &\Rightarrow \frac{d y}{d x}(\text { at } x=e)=\frac{f^{\prime}\left(\log _{e} e\right)}{e} \\\\ &=\frac{f^{{}'}1}{e} \text { since } f^{{}'} 1=2 \\\\ &=\frac{2}{e} \end{aligned}

∴So, the answer will be \frac{2}{e}

 

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