derivative of (x^2/(5+6x))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{5 + 6 x})

\frac{10 x + 6 x ^{2}}{( 5 + 6 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{5 + 6 x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 5 + 6 x ) - \frac{d}{d x} ( 5 + 6 x ) x ^{2}}{( 5 + 6 x ) ^{2}}

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

\frac{d}{d x} (5 + 6 x) = 6

= \frac{2 x ( 5 + 6 x ) - 6 x ^{2}}{( 5 + 6 x ) ^{2}}

Multipliziere aus

2 x (5 + 6 x) - 6 x^{2} : 10 x + 6 x^{2}

= \frac{10 x + 6 x ^{2}}{( 5 + 6 x ) ^{2}}

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