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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 find $\frac{d y}{d x}$.
  • A
    $-e^x \tan ^2 x$
  • B
    $e^x \tan x$
  • C
    $e^x \sec x$
  • ✓
    $-e^x \tan x$
✓

Answer

Correct option: D.
$-e^x \tan x$
(d): Given, $y=\log \left(\cos e^x\right)$
On differentiating w.r.t. $x$, we get
$
\frac{d y}{d x}=\frac{1}{\cos e^x}\left(-\sin e^x \cdot e^x\right)=-e^x \tan e^x
$

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