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Beliebt Rechnen >

derivative r/(sqrt(r^2+4))

Lösung

ableitung von

\frac{r}{r ^{2} + 4}

Lösung

\frac{4}{( r ^{2} + 4 ) r ^{2} + 4}

Schritte zur Lösung

\frac{d}{d r} (\frac{r}{r ^{2} + 4})

Wende die Quotientenregel an:

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

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

\frac{d r}{d r} = 1

\frac{d}{d r} (r^{2} + 4) = \frac{r}{r ^{2} + 4}

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

Vereinfache

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

= \frac{4}{( r ^{2} + 4 ) r ^{2} + 4}

Graph

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