derivative y=sqrt(x(x+2))

解

導関数

y = x (x + 2)

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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