derivative y=(x^2-2sqrt(x))/x

解

導関数

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

\frac{x ^{2} + x}{x ^{2}}

解答ステップ

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

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

\frac{d x}{d x} = 1

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

簡素化

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

= \frac{x ^{2} + x}{x ^{2}}