Question

If f'(x) = cosx e^sinx then what is its exact value of f'(Pie/6)????

Answer 1

What is \(\cos(\frac{\pi}{6})\)?

Answer 2

The answer is square root of 3e/2 but I still don't get it

Answer 3

\[cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}\]\[sin(\frac{\pi}{6})= \frac{1}{2}\]

\[f'(\frac{\pi}{6})=cos(\frac{\pi}{6}) e^{sin(\frac{\pi}{6})}=\frac{\sqrt{3}}{2}e^{\frac{1}{2}}=\frac{\sqrt{3}}{2}(\sqrt{e})=\frac{\sqrt{3e}}{2}\]