Cho hàm số y=cos3x.sin2x. tính y'(pi/3) bằng

* Hướng dẫn giải

Chọn B

$\begin{array}{l}y\text{'}=\left(\cos 3x\right)\text{'}\sin 2x+\cos 3x\left(\sin 2x\right)\text{'}\\ =-3\sin 3x.\sin 2x+2\cos 3x.\cos 2x\end{array}$

$\begin{array}{l}y\text{'}\left(\frac{\pi }{3}\right)\\ =-3\sin 3\frac{\pi }{3}.\sin 2\frac{\pi }{3}+2\cos 3\frac{\pi }{3}.\cos 2\frac{\pi }{3}\\ =-\mathrm{3.0.}\frac{\sqrt{3}}{2}+\text{}2.(-1).\frac{-1}{2}=1\end{array}$