derivative sqrt(2e^{x^3)+1}

解

導関数

2 e^{x^{3}} + 1

\frac{3 e ^{x^{3}} x ^{2}}{2 e ^{x^{3}} + 1}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (2 e^{x^{3}} + 1) = 6 e^{x^{3}} x^{2}

= \frac{1}{2 2 e ^{x^{3}} + 1} \cdot 6 e^{x^{3}} x^{2}

簡素化

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

= \frac{3 e ^{x^{3}} x ^{2}}{2 e ^{x^{3}} + 1}