derivative (x^2-3)/(x-2)

Lösung

ableitung von

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

\frac{x ^{2} - 4 x + 3}{( x - 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x ( x - 2 ) - 1 \cdot ( x ^{2} - 3 )}{( x - 2 ) ^{2}} : \frac{x ^{2} - 4 x + 3}{( x - 2 ) ^{2}}

= \frac{x ^{2} - 4 x + 3}{( x - 2 ) ^{2}}

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