derivative f(x)= x/(x-3)

Lösung

ableitung von

f (x) = \frac{x}{x - 3}

- \frac{3}{( x - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x - 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x - 3 ) - \frac{d}{d x} ( x - 3 ) x}{( x - 3 ) ^{2}}

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

\frac{d}{d x} (x - 3) = 1

= \frac{1 \cdot ( x - 3 ) - 1 \cdot x}{( x - 3 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x - 3 ) - 1 \cdot x}{( x - 3 ) ^{2}} : - \frac{3}{( x - 3 ) ^{2}}

= - \frac{3}{( x - 3 ) ^{2}}

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