derivative of sqrt(x^2+e^{\sqrt{x)}}

解

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

\frac{4 x x + e ^{x}}{4 x x ^{2} + e ^{x}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 x ^{2} + e ^{x}} (2 x + \frac{e ^{x}}{2 x}) : \frac{4 x x + e ^{x}}{4 x x ^{2} + e ^{x}}

= \frac{4 x x + e ^{x}}{4 x x ^{2} + e ^{x}}