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

解

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

- 2 sin^{2} (x) + cos (x) (1 + 2 cos (x))

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

(- 2 sin (x)) sin (x) + cos (x) (1 + 2 cos (x)) : - 2 sin^{2} (x) + cos (x) (1 + 2 cos (x))

= - 2 sin^{2} (x) + cos (x) (1 + 2 cos (x))