derivative of sqrt(4/9 x^3)

解

\frac{d}{d x} (\frac{4}{9} x^{3})

x

解答ステップ

\frac{d}{d x} (\frac{4}{9} x^{3})

連鎖法則を適用:

\frac{1}{2 \frac{4}{9} x ^{3}} \frac{d}{d x} (\frac{4}{9} x^{3})

= \frac{1}{2 \frac{4}{9} x ^{3}} \frac{d}{d x} (\frac{4}{9} x^{3})

\frac{d}{d x} (\frac{4}{9} x^{3}) = \frac{4 x ^{2}}{3}

= \frac{1}{2 \frac{4}{9} x ^{3}} \cdot \frac{4 x ^{2}}{3}

簡素化

\frac{1}{2 \frac{4}{9} x ^{3}} \cdot \frac{4 x ^{2}}{3} : x

= x