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

解

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

\frac{4 x ( x ^{2} + 2 )}{9}

解答ステップ

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

連鎖法則を適用:

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

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

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

= 2 \cdot \frac{x ^{2} + 2}{3} \cdot \frac{2 x}{3}

簡素化

2 \cdot \frac{x ^{2} + 2}{3} \cdot \frac{2 x}{3} : \frac{4 x ( x ^{2} + 2 )}{9}

= \frac{4 x ( x ^{2} + 2 )}{9}