derivative ((x^2))/(5+x)

解

導関数

\frac{( x ^{2} )}{5 + x}

\frac{10 x + x ^{2}}{( 5 + x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x ^{2}}{5 + x})

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 ^{2} ) ( 5 + x ) - \frac{d}{d x} ( 5 + x ) x ^{2}}{( 5 + x ) ^{2}}

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

\frac{d}{d x} (5 + x) = 1

= \frac{2 x ( 5 + x ) - 1 \cdot x ^{2}}{( 5 + x ) ^{2}}

簡素化

\frac{2 x ( 5 + x ) - 1 \cdot x ^{2}}{( 5 + x ) ^{2}} : \frac{10 x + x ^{2}}{( 5 + x ) ^{2}}

= \frac{10 x + x ^{2}}{( 5 + x ) ^{2}}