derivative of (94x/(99x-94))

Lösung

\frac{d}{d x} (\frac{94 x}{99 x - 94})

- \frac{8836}{( 99 x - 94 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{94 x}{99 x - 94})

Entferne die Konstante:

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

= 94 \frac{d}{d x} (\frac{x}{99 x - 94})

Wende die Quotientenregel an:

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

= 94 \cdot \frac{\frac{d x}{d x} ( 99 x - 94 ) - \frac{d}{d x} ( 99 x - 94 ) x}{( 99 x - 94 ) ^{2}}

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

\frac{d}{d x} (99 x - 94) = 99

= 94 \cdot \frac{1 \cdot ( 99 x - 94 ) - 99 x}{( 99 x - 94 ) ^{2}}

Vereinfache

94 \cdot \frac{1 \cdot ( 99 x - 94 ) - 99 x}{( 99 x - 94 ) ^{2}} : - \frac{8836}{( 99 x - 94 ) ^{2}}

= - \frac{8836}{( 99 x - 94 ) ^{2}}

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