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

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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