derivative of (1+sin(x)*cos(2x))

解

\frac{d}{d x} ((1 + sin (x)) \cdot cos (2 x))

cos (x) cos (2 x) - 2 sin (2 x) (1 + sin (x))

解答ステップ

\frac{d}{d x} ((1 + sin (x)) cos (2 x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 + sin (x), g = cos (2 x)

= \frac{d}{d x} (1 + sin (x)) cos (2 x) + \frac{d}{d x} (cos (2 x)) (1 + sin (x))

\frac{d}{d x} (1 + sin (x)) = cos (x)

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= cos (x) cos (2 x) + (- sin (2 x) \cdot 2) (1 + sin (x))

簡素化

= cos (x) cos (2 x) - 2 sin (2 x) (1 + sin (x))