derivative sin(7x)sin(2x)

解

導関数

sin (7 x) sin (2 x)

cos (7 x) \cdot 7 sin (2 x) + cos (2 x) \cdot 2 sin (7 x)

解答ステップ

\frac{d}{d x} (sin (7 x) sin (2 x))

積の法則を適用:

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

f = sin (7 x), g = sin (2 x)

= \frac{d}{d x} (sin (7 x)) sin (2 x) + \frac{d}{d x} (sin (2 x)) sin (7 x)

\frac{d}{d x} (sin (7 x)) = cos (7 x) \cdot 7

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

= cos (7 x) \cdot 7 sin (2 x) + cos (2 x) \cdot 2 sin (7 x)