derivative of x/(6-x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (6 - x) = - 1

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

Vereinfache

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

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

x \to 2 lim (8 - 3 x + 12 x^{2})

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