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Beliebt Rechnen >

derivative of (x^2/(3+4x))

Lösung

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

Lösung

\frac{6 x + 4 x ^{2}}{( 3 + 4 x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (3 + 4 x) = 4

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

Multipliziere aus

2 x (3 + 4 x) - 4 x^{2} : 6 x + 4 x^{2}

= \frac{6 x + 4 x ^{2}}{( 3 + 4 x ) ^{2}}

Graph

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