I was solving some A Level past papers and I came across this question. We have the equation of the line $ y=\sin^2(2x)\cos(x) $ for $ 0\leq x \leq \frac{\pi}{2} $ and there is a maximum point M. We need to find the x coordinate of M. I know that at maximum points, the $dy/dx$ would be 0 which would help us find M. However, I am unable to differentiate this equation. I used the rule $dy/dx=u'v+v'u$ where u and v are functions of x, but am getting the wrong answer. I would really appreciate if someone would guide me through this question and give me the answer. I tried WolframAlpha but am a free member so I won't get step-by-step instructions, and the paper's mark scheme doesn't have a good explanation of steps. Thanks!
[Math] How to differentiate $ y=\sin^2(2x)\cos(x) $
algebraic-curvescalculusderivativestrigonometry
Best Answer
Hint: $$\frac{dy}{dx} = {\sin^2(2x)}\left(-\sin(x)\right) + {\cos(x)}\left(2\sin(2x)\cos(2x)\right)\cdot{2}$$
Can you take it from here?