derivative f(x)=(x^2+3)/(x^2)

解

導関数

f (x) = \frac{x ^{2} + 3}{x ^{2}}

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

解答ステップ

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

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

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

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

簡素化

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

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