d/(d{r)}((120{r})/({r)+120})

Lösung

\frac{d}{d r} (\frac{120 r}{r + 120})

\frac{14400}{( r + 120 ) ^{2}}

Schritte zur Lösung

\frac{d}{d r} (\frac{120 r}{r + 120})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 120 \frac{d}{d r} (\frac{r}{r + 120})

Wende die Quotientenregel an:

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

= 120 \cdot \frac{\frac{d}{d r} ( r ) ( r + 120 ) - \frac{d}{d r} ( r + 120 ) r}{( r + 120 ) ^{2}}

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

\frac{d}{d r} (r + 120) = 1

= 120 \cdot \frac{1 \cdot ( r + 120 ) - 1 \cdot r}{( r + 120 ) ^{2}}

Vereinfache

120 \cdot \frac{1 \cdot ( r + 120 ) - 1 \cdot r}{( r + 120 ) ^{2}} : \frac{14400}{( r + 120 ) ^{2}}

= \frac{14400}{( r + 120 ) ^{2}}

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