Question

If $y=e^{\cos x}$, find $\frac{dy}{dx}$.

Answer 1

$y=e^{cosx}$

Taking log both sides, we get

$\log y=\cos x\log e$

Differentiating both sides w.r.t x, we get $\frac{1}{y}\frac{dy}{dx}=-\sin x.loge$

$\frac{dy}{dx}=y(\log e.(-\sin x\left)\right)$

$\frac{dy}{dx}=-\log e{e}^{\cos x}.sinx$