derivative of (x+3/(x^2))

解

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

\frac{- x - 6}{x ^{3}}

解答ステップ

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

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

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

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

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

簡素化

\frac{1 \cdot x ^{2} - 2 x ( x + 3 )}{( x ^{2} ) ^{2}} : \frac{- x - 6}{x ^{3}}

= \frac{- x - 6}{x ^{3}}