If y= ( e^x ), then d y d x is - Vidyadip

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
$e^x \sin e^x$
D
$-e^x \tan e^x$

✓

Answer

We have, $y=\log \left(\cos e^x\right)$
Differentiating both sides w.r.t. $x$, we get
$
\begin{array}{l}
\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
\end{array}
$

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