derivative of-x/(sqrt(4-x^2))

解

\frac{d}{d x} (- \frac{x}{4 - x ^{2}})

- \frac{4}{( 4 - x ^{2} ) 4 - x ^{2}}

解答ステップ

\frac{d}{d x} (- \frac{x}{4 - x ^{2}})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (\frac{x}{4 - x ^{2}})

商の法則を適用:

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

= - \frac{\frac{d x}{d x} 4 - x ^{2} - \frac{d}{d x} ( 4 - x ^{2} ) x}{( 4 - x ^{2} ) ^{2}}

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

\frac{d}{d x} (4 - x^{2}) = - \frac{x}{4 - x ^{2}}

= - \frac{1 \cdot 4 - x ^{2} - ( - \frac{x}{4 - x ^{2}} ) x}{( 4 - x ^{2} ) ^{2}}

簡素化

- \frac{1 \cdot 4 - x ^{2} - ( - \frac{x}{4 - x ^{2}} ) x}{( 4 - x ^{2} ) ^{2}} : - \frac{4}{( 4 - x ^{2} ) 4 - x ^{2}}

= - \frac{4}{( 4 - x ^{2} ) 4 - x ^{2}}