Solve this

Question:

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

Solution:

$y=f\left(\log _{e} x\right)$

Using the Chain Rule of Differentiation,

$\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{f}^{\prime}\left(\log _{\mathrm{e}} \mathrm{x}\right) \cdot \frac{1}{\mathrm{x}}$

So, at $\mathrm{x}=\mathrm{e}$

$\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{f}^{\prime}\left(\log _{\mathrm{e}} \mathrm{e}\right) \cdot \frac{1}{\mathrm{e}}$

$=f^{\prime}(1) \cdot \frac{1}{e}$

$=\frac{2}{e}($ Ans $)$

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now