derivative of y/(x^2)

解

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

\frac{x \frac{d y}{d x} - 2 y}{x ^{3}}

解答ステップ

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

商の法則を適用:

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

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

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

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

簡素化

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

= \frac{x \frac{d y}{d x} - 2 y}{x ^{3}}