(sin(x)sin(2x)sin(3x))^'

解

(sin (x) sin (2 x) sin (3 x))^{^{'}}

cos (x) sin (2 x) sin (3 x) + (cos (2 x) \cdot 2 sin (3 x) + cos (3 x) \cdot 3 sin (2 x)) sin (x)

解答ステップ

(sin (x) sin (2 x) sin (3 x))^{'}

積の法則を適用:

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

f = sin (x), g = sin (2 x) sin (3 x)

= (sin (x))^{^{'}} sin (2 x) sin (3 x) + (sin (2 x) sin (3 x))^{^{'}} sin (x)

(sin (x))^{'} = cos (x)

(sin (2 x) sin (3 x))^{'} = cos (2 x) \cdot 2 sin (3 x) + cos (3 x) \cdot 3 sin (2 x)

= cos (x) sin (2 x) sin (3 x) + (cos (2 x) \cdot 2 sin (3 x) + cos (3 x) \cdot 3 sin (2 x)) sin (x)