derivative sqrt(x/(x+3))

解

導関数

\frac{x}{x + 3}

\frac{3}{2 x ( x + 3 ) ^{\frac{3}{2}}}

解答ステップ

\frac{d}{d x} (\frac{x}{x + 3})

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 \frac{x}{x + 3}} \cdot \frac{3}{( x + 3 ) ^{2}} : \frac{3}{2 x ( x + 3 ) ^{\frac{3}{2}}}

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