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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $y=\log \left(\cos e^x\right)$, then $\frac{d y}{d x}$ is
  • A
    $\cos e^{x-1}$
  • B
    $e^{-x} \cos e^x$
  • C
    $e^x \sin e^x$
  • ✓
    $-e^x \tan e^x$
✓

Answer

Correct option: D.
$-e^x \tan e^x$
We have, $y=\log \left(\cos e^x\right)$
Differentiating both sides w.r.t. $x$, we get
$\frac{d y}{d x}=\frac{1}{\cos e^x} \cdot\left(-\sin e^x\right) \cdot e^x$
$\Rightarrow \frac{d y}{d x}=-e^x \tan e^x$

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