`~rai~`
\(y=x.\sin2x\\\Rightarrow y'=x'.\sin2x+x.(\sin2x)'\\\quad\quad=1.\sin2x+x.\cos2x.(2x)'\\\quad\quad=\sin2x+x\cos2x.2\\\quad\quad=\sin2x+2x\cos2x.\\\Rightarrow y'\left(\dfrac{\pi}{4}\right)=\sin\left(2.\dfrac{\pi}{4}\right)+2.\dfrac{\pi}{4}.\cos\left(2.\dfrac{\pi}{4}\right)\\\quad\quad\quad\quad\quad=\sin\dfrac{\pi}{2}+\dfrac{\pi}{2}.\cos\dfrac{\pi}{2}=1+\dfrac{\pi}{2}.0=1.\\\text{Vậy }y'\left(\dfrac{\pi}{4}\right)=1.\\\text{Áp dụng công thức:}\\+)(u.v)'=u'.v+u.v'\\+)x'=1\\+)(\sin u)'=u'.\cos u.\)
