derivative h(x)=5sin^3(3+x)

解

導関数

h (x) = 5 sin^{3} (3 + x)

15 sin^{2} (3 + x) cos (3 + x)

解答ステップ

\frac{d}{d x} (5 sin^{3} (3 + x))

定数を除去:

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

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

連鎖法則を適用:

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

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

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

= 5 \cdot 3 (sin (3 + x))^{2} cos (3 + x)

簡素化

= 15 sin^{2} (3 + x) cos (3 + x)