derivative of sqrt(x^3+10)

解

\frac{d}{d x} (x^{3} + 10)

\frac{3 x ^{2}}{2 x ^{3} + 10}

解答ステップ

\frac{d}{d x} (x^{3} + 10)

連鎖法則を適用:

\frac{1}{2 x ^{3} + 10} \frac{d}{d x} (x^{3} + 10)

= \frac{1}{2 x ^{3} + 10} \frac{d}{d x} (x^{3} + 10)

\frac{d}{d x} (x^{3} + 10) = 3 x^{2}

= \frac{1}{2 x ^{3} + 10} \cdot 3 x^{2}

簡素化

\frac{1}{2 x ^{3} + 10} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 x ^{3} + 10}

= \frac{3 x ^{2}}{2 x ^{3} + 10}