derivative of sqrt(4x^3+2)

解

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

\frac{6 x ^{2}}{4 x ^{3} + 2}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (4 x^{3} + 2) = 12 x^{2}

= \frac{1}{2 4 x ^{3} + 2} \cdot 12 x^{2}

簡素化

\frac{1}{2 4 x ^{3} + 2} \cdot 12 x^{2} : \frac{6 x ^{2}}{4 x ^{3} + 2}

= \frac{6 x ^{2}}{4 x ^{3} + 2}