Question

$when f(x)=e^{sin(x)}$
$Find f'(\frac{\pi }{6} )$

Answer 1

$f(x)=e^{\sin(x)}\\\\f'(x)=\left(e^{\sin(x)}\right)'=e^{\sin(x)}\cdot\cos(x)\\\\f'\left(\dfrac{\pi}{6}\right)=e^{\sin\left(\frac{\pi}{6}\right)}\cdot\cos\left(\dfrac{\pi}{6}\right)=e^{\frac{1}{2}}\cdot\dfrac{\sqrt3}{2}=\sqrt{e}\cdot\dfrac{\sqrt3}{2}=\dfrac{\sqrt{3e}}{2}$

$Used:\\\\(e^x)'=e^x\\\\\{f[g(x)]\}'=f'[g(x)]\cdot g'(x)$