How derivate this? Please help me

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Answer 1 · 2017-08-15T13:14:03

$f'(x) = cos(x) cos(2 x) - 2 sin(x) sin(2 x)$

I believe you mean $f(x) = sin(x) cdot cos(2 x)$

We can differentiate this function using the chain rule and the product rule.

Let $u = 2 x Rightarrow u' = 2$ and $v = cos(u) Rightarrow v' = - sin(u)$ :

$Rightarrow f'(x) = frac(d)(dx)(sin(x)) cdot (cos(2 x)) + frac(d)(dx)(cos(2 x)) cdot (sin(x))$

$Rightarrow f'(x) = cos(x) cdot cos(2 x) + u' cdot v' cdot sin(x)$

$Rightarrow f'(x) = cos(x) cos(2 x) + 2 cdot - sin(u) cdot sin(x)$

$Rightarrow f'(x) = cos(x) cos(2 x) - 2 sin(u) sin(x)$

Let's replace $u$ with $2 x$ :

$Rightarrow f'(x) = cos(x) cos(2 x) - 2 sin(2 x) sin(x)$

$therefore f'(x) = cos(x) cos(2 x) - 2 sin(x) sin(2 x)$