derivative of sqrt(x^2+8x)

解

\frac{d}{d x} (x^{2} + 8 x)

\frac{x + 4}{x ^{2} + 8 x}

解答ステップ

\frac{d}{d x} (x^{2} + 8 x)

連鎖法則を適用:

\frac{1}{2 x ^{2} + 8 x} \frac{d}{d x} (x^{2} + 8 x)

= \frac{1}{2 x ^{2} + 8 x} \frac{d}{d x} (x^{2} + 8 x)

\frac{d}{d x} (x^{2} + 8 x) = 2 x + 8

= \frac{1}{2 x ^{2} + 8 x} (2 x + 8)

簡素化

\frac{1}{2 x ^{2} + 8 x} (2 x + 8) : \frac{x + 4}{x ^{2} + 8 x}

= \frac{x + 4}{x ^{2} + 8 x}