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

解

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

\frac{18 x ( x ^{2} + 2 ) ^{2}}{5}

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

\frac{3}{5} \cdot 3 (x^{2} + 2)^{2} \cdot 2 x : \frac{18 x ( x ^{2} + 2 ) ^{2}}{5}

= \frac{18 x ( x ^{2} + 2 ) ^{2}}{5}