Question

if f(x)=sinx(cos-1),find f'(a)if a=pi*

Answer 1

\[f'(x)=\sin{x}(-\sin{x})+\cos{x}(\cos{x}-1)\]\[=\cos^2{x}-\sin^2{x}-\cos{x}\]\[=\cos{2x}-\cos{x}\]Then,\[f'(\pi)=\cos{2\pi}-\cos{\pi}=1-(-1)=2\]