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Beliebt Rechnen >

derivative (s^2-4)/(s+1)

Lösung

ableitung von

\frac{s ^{2} - 4}{s + 1}

Lösung

\frac{s ^{2} + 2 s + 4}{( s + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d s} (\frac{s ^{2} - 4}{s + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d s} ( s ^{2} - 4 ) ( s + 1 ) - \frac{d}{d s} ( s + 1 ) ( s ^{2} - 4 )}{( s + 1 ) ^{2}}

\frac{d}{d s} (s^{2} - 4) = 2 s

\frac{d}{d s} (s + 1) = 1

= \frac{2 s ( s + 1 ) - 1 \cdot ( s ^{2} - 4 )}{( s + 1 ) ^{2}}

Vereinfache

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

= \frac{s ^{2} + 2 s + 4}{( s + 1 ) ^{2}}

Graph

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