Question

show that dy/dx, x=pi, xsin(x)cos(x) = pi in a MINIMUM OF 3 STEPS.

i messed up when trying to do it. i know you need to do the product rule in a product rule.

Answer 1

\[f(x)=x\sin{x}\cos{x}=\frac{x}{2}\sin{2x}\]\[f'(x)=\left(\frac{x}{2}\right)'\sin{2x}+\frac{x}{2}(\sin{2x})'=\frac{1}{2}\sin{2x}+x\cos{2x}\]\[f'(\pi)=\frac{1}{2}\sin{2\pi}+\pi\cos{2\pi}=\pi\]