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Beliebt Rechnen >

derivative of ((x^2-5^3)/(x^2+4))

Lösung

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{x ^{2} + 4})

Lösung

\frac{6 x ( x ^{2} - 5 ) ^{2} ( x ^{2} + 4 ) - 2 x ( x ^{2} - 5 ) ^{3}}{( x ^{2} + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{x ^{2} + 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x ^{2} - 5 ) ^{3} ) ( x ^{2} + 4 ) - \frac{d}{d x} ( x ^{2} + 4 ) ( x ^{2} - 5 ) ^{3}}{( x ^{2} + 4 ) ^{2}}

\frac{d}{d x} ((x^{2} - 5)^{3}) = 6 x (x^{2} - 5)^{2}

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

= \frac{6 x ( x ^{2} - 5 ) ^{2} ( x ^{2} + 4 ) - 2 x ( x ^{2} - 5 ) ^{3}}{( x ^{2} + 4 ) ^{2}}

Graph

Beliebte Beispiele

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steigung (4.5)(2.3)

s l o p e (4.5) (2.3)

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