derivative (sqrt(9-x^2))/(4x)

Lösung

ableitung von

\frac{9 - x ^{2}}{4 x}

- \frac{9}{4 x ^{2} 9 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9 - x ^{2}}{4 x})

Entferne die Konstante:

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

= \frac{1}{4} \frac{d}{d x} (\frac{9 - x ^{2}}{x})

Wende die Quotientenregel an:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( 9 - x ^{2} ) x - \frac{d x}{d x} 9 - x ^{2}}{x ^{2}}

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

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

= \frac{1}{4} \cdot \frac{( - \frac{x}{9 - x ^{2}} ) x - 1 \cdot 9 - x ^{2}}{x ^{2}}

Vereinfache

\frac{1}{4} \cdot \frac{( - \frac{x}{9 - x ^{2}} ) x - 1 \cdot 9 - x ^{2}}{x ^{2}} : - \frac{9}{4 x ^{2} 9 - x ^{2}}

= - \frac{9}{4 x ^{2} 9 - x ^{2}}

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