derivative of sin(2xcos(3x))

解

\frac{d}{d x} (sin (2 x) cos (3 x))

2 cos (2 x) cos (3 x) - 3 sin (3 x) sin (2 x)

解答ステップ

\frac{d}{d x} (sin (2 x) cos (3 x))

積の法則を適用:

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

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

= \frac{d}{d x} (sin (2 x)) cos (3 x) + \frac{d}{d x} (cos (3 x)) sin (2 x)

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

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

簡素化

= 2 cos (2 x) cos (3 x) - 3 sin (3 x) sin (2 x)