Search any question & find its solution
Question:
Answered & Verified by Expert
If $\mathrm{y}=\frac{1}{\log _{10} \mathrm{x}}$, then what is $\frac{\mathrm{dy}}{\mathrm{dx}}$ equal to?
Options:
Solution:
2160 Upvotes
Verified Answer
The correct answer is:
$-\frac{\left(\log _{x} 10\right)^{2}\left(\log _{10} e\right)}{x}$
Differentiating the given function, $\mathrm{y}=\frac{1}{\log _{10} \mathrm{x}}$
We get, $\frac{d y}{d x}=-\frac{1}{\left(\log _{10} x\right)^{2}} \cdot \frac{1}{x} \log _{10} e$
$\Rightarrow \frac{d y}{d x}=-\frac{\left(\log _{x} 10\right)^{2} \cdot \log _{10} e}{x}$
We get, $\frac{d y}{d x}=-\frac{1}{\left(\log _{10} x\right)^{2}} \cdot \frac{1}{x} \log _{10} e$
$\Rightarrow \frac{d y}{d x}=-\frac{\left(\log _{x} 10\right)^{2} \cdot \log _{10} e}{x}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.