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Differentiation (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Differentiation (p-1)3 Marks
Question
Find $\frac{d y}{d x}$ if, :
$
y=5^{(x+\log x)}
$
✓

Answer

Given : $y=5^{(x+\log x)}$
Let $u=x+\log x$
Then $y=5^u$
$
\begin{aligned}
& \therefore \frac{d y}{d u}=\frac{d}{d u}\left(5^u\right)=5^u \cdot \log 5 \\
& =5^{(x+\log x)} \cdot \log 5 \\
& \text { and } \frac{d u}{d x}=\frac{d}{d x}(x+\log x) \\
& =1+\frac{1}{x} \\
& \therefore \frac{d y}{d x}=\frac{d y}{d u} \cdot \frac{d u}{d x} \\
& =5^{(x+\log x)} \cdot \log 5 \cdot\left(1+\frac{1}{x}\right) . \\
\end{aligned}
$

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