Question

`when f(x)=e^(sin(x))`

`Find f'((\pi )/(6) )`

Answer 1

`f(x)=e^(\sin(x))\\\\f'(x)=\left(e^(\sin(x))\right)'=e^(\sin(x))\cdot\cos(x)\\\\f'\left((\pi)/(6)\right)=e^{\sin\left((\pi)/(6)\right)}\cdot\cos\left((\pi)/(6)\right)=e^{(1)/(2)}\cdot(\sqrt3)/(2)=√(e)\cdot(\sqrt3)/(2)=(√(3e))/(2)`

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