If y= ( e^x ), then find d y d x .

Question

If $y=\log \left(\cos e^x\right)$, then find $\frac{d y}{d x}$.

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Answer

(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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