derivative f(x)=(6-x^2)/(sqrt(x))

解

導関数

f (x) = \frac{6 - x ^{2}}{x}

\frac{- 3 x ^{2} - 6}{2 x x}

解答ステップ

\frac{d}{d x} (\frac{6 - x ^{2}}{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} ( 6 - x ^{2} ) x - \frac{d}{d x} ( x ) ( 6 - x ^{2} )}{( x ) ^{2}}

\frac{d}{d x} (6 - x^{2}) = - 2 x

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

= \frac{( - 2 x ) x - \frac{1}{2 x} ( 6 - x ^{2} )}{( x ) ^{2}}

簡素化

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

= \frac{- 3 x ^{2} - 6}{2 x x}