derivative of 1/3 cos^3(x)

解

\frac{d}{d x} (\frac{1}{3} cos^{3} (x))

- cos^{2} (x) sin (x)

解答ステップ

\frac{d}{d x} (\frac{1}{3} cos^{3} (x))

定数を除去:

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

= \frac{1}{3} \frac{d}{d x} (cos^{3} (x))

連鎖法則を適用:

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

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

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

= \frac{1}{3} \cdot 3 (cos (x))^{2} (- sin (x))

簡素化

\frac{1}{3} \cdot 3 cos^{2} (x) (- sin (x)) : - cos^{2} (x) sin (x)

= - cos^{2} (x) sin (x)