derivative of 1/2 (cos(5x)^2)

解

\frac{d}{d x} (\frac{1}{2} (cos (5 x))^{2})

- \frac{5 sin ( 10 x )}{2}

解答ステップ

\frac{d}{d x} (\frac{1}{2} (cos (5 x))^{2})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} ((cos (5 x))^{2})

連鎖法則を適用:

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

= 2 cos (5 x) \frac{d}{d x} (cos (5 x))

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

= \frac{1}{2} \cdot 2 cos (5 x) (- sin (5 x) \cdot 5)

簡素化

\frac{1}{2} \cdot 2 cos (5 x) (- sin (5 x) \cdot 5) : - \frac{5 sin ( 10 x )}{2}

= - \frac{5 sin ( 10 x )}{2}