derivative 9cos^3(x)

解

導関数

9 cos^{3} (x)

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

解答ステップ

\frac{d}{d x} (9 cos^{3} (x))

定数を除去:

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

= 9 \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)

= 9 \cdot 3 (cos (x))^{2} (- sin (x))

簡素化

= - 27 cos^{2} (x) sin (x)