derivative of (a+bx^2/(x^2))

解

\frac{d}{d x} (\frac{a + b x ^{2}}{x ^{2}})

- \frac{2 a}{x ^{3}}

解答ステップ

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

\frac{d}{d x} (a + b x^{2}) = 2 b x

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

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

簡素化

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

= - \frac{2 a}{x ^{3}}