derivative 3(x^2+5x)^3

解

導関数

3 (x^{2} + 5 x)^{3}

9 (x^{2} + 5 x)^{2} (2 x + 5)

解答ステップ

\frac{d}{d x} (3 (x^{2} + 5 x)^{3})

定数を除去:

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

= 3 \frac{d}{d x} ((x^{2} + 5 x)^{3})

連鎖法則を適用:

3 (x^{2} + 5 x)^{2} \frac{d}{d x} (x^{2} + 5 x)

= 3 (x^{2} + 5 x)^{2} \frac{d}{d x} (x^{2} + 5 x)

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

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

簡素化

= 9 (x^{2} + 5 x)^{2} (2 x + 5)