derivative of-x/(sqrt(9-x^2))

Lösung

\frac{d}{d x} (- \frac{x}{9 - x ^{2}})

- \frac{9}{( 9 - x ^{2} ) 9 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{x}{9 - x ^{2}})

Entferne die Konstante:

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

= - \frac{d}{d x} (\frac{x}{9 - x ^{2}})

Wende die Quotientenregel an:

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

= - \frac{\frac{d x}{d x} 9 - x ^{2} - \frac{d}{d x} ( 9 - x ^{2} ) x}{( 9 - x ^{2} ) ^{2}}

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

\frac{d}{d x} (9 - x^{2}) = - \frac{x}{9 - x ^{2}}

= - \frac{1 \cdot 9 - x ^{2} - ( - \frac{x}{9 - x ^{2}} ) x}{( 9 - x ^{2} ) ^{2}}

Vereinfache

- \frac{1 \cdot 9 - x ^{2} - ( - \frac{x}{9 - x ^{2}} ) x}{( 9 - x ^{2} ) ^{2}} : - \frac{9}{( 9 - x ^{2} ) 9 - x ^{2}}

= - \frac{9}{( 9 - x ^{2} ) 9 - x ^{2}}

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