derivative cos(3x)cos(5*x)

解

導関数

cos (3 \cdot x) \cdot cos (5 \cdot x)

- 3 sin (3 x) cos (5 x) - 5 sin (5 x) cos (3 x)

解答ステップ

\frac{d}{d x} (cos (3 x) cos (5 x))

積の法則を適用:

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

f = cos (3 x), g = cos (5 x)

= \frac{d}{d x} (cos (3 x)) cos (5 x) + \frac{d}{d x} (cos (5 x)) cos (3 x)

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

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= (- sin (3 x) \cdot 3) cos (5 x) + (- sin (5 x) \cdot 5) cos (3 x)

簡素化

= - 3 sin (3 x) cos (5 x) - 5 sin (5 x) cos (3 x)