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

解

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

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

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2 x) = 2

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

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