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Differentiation (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Differentiation (p-1)1 Mark
Question
Differentiate the following functions w.r.t. x. : $\frac{2^x}{\log x}$
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Answer

Let $y=\frac{2^x}{\log x}$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{\mathrm{d} y}{\mathrm{~d} x} & =\frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{2^x}{\log x}\right) \\
& =\frac{\log x \frac{\mathrm{d}}{\mathrm{d} x}\left(2^x\right)-2^x \frac{\mathrm{d}}{\mathrm{d} x}(\log x)}{(\log x)^2} \\
& =\frac{\log x\left(2^x \log 2\right)-2^x\left(\frac{1}{x}\right)}{(\log x)^2} \\
& =\frac{\left(2^x \log x \cdot \log 2\right)\left(-\frac{1}{x}\right)}{(\log x)^2}
\end{aligned}
$

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