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Beliebt Rechnen >

derivative of (4x^2+5/(x^2+7))

Lösung

\frac{d}{d x} (\frac{4 x ^{2} + 5}{x ^{2} + 7})

Lösung

\frac{46 x}{( x ^{2} + 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{2} + 5}{x ^{2} + 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} + 5 ) ( x ^{2} + 7 ) - \frac{d}{d x} ( x ^{2} + 7 ) ( 4 x ^{2} + 5 )}{( x ^{2} + 7 ) ^{2}}

\frac{d}{d x} (4 x^{2} + 5) = 8 x

\frac{d}{d x} (x^{2} + 7) = 2 x

= \frac{8 x ( x ^{2} + 7 ) - 2 x ( 4 x ^{2} + 5 )}{( x ^{2} + 7 ) ^{2}}

Multipliziere aus

8 x (x^{2} + 7) - 2 x (4 x^{2} + 5) : 46 x

= \frac{46 x}{( x ^{2} + 7 ) ^{2}}

Graph

Beliebte Beispiele

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