derivative (sqrt(x))/(x+3)

解

導関数

\frac{x}{x + 3}

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

解答ステップ

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

簡素化

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

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