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Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
If $y=\cos ^{-1}\left(e^x\right)$, then $\frac{d y}{d x}$ is :
✓

Answer

We have, $y=\cos ^{-1}\left(e^x\right)$
$\Rightarrow \frac{d y}{d x}=\frac{-1}{\sqrt{1-\left(e^x\right)^2}} e^x=\frac{-e^x}{\sqrt{1-e^{2 x}}}=\frac{-e^x}{e^x \sqrt{e^{-2 x}-1}}=\frac{-1}{\sqrt{e^{-2 x}-1}}$

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