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Beliebt Rechnen >

derivative of (x^2+1/(x-9))

Lösung

\frac{d}{d x} (\frac{x ^{2} + 1}{x - 9})

Lösung

\frac{x ^{2} - 18 x - 1}{( x - 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 1}{x - 9})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 1 ) ( x - 9 ) - \frac{d}{d x} ( x - 9 ) ( x ^{2} + 1 )}{( x - 9 ) ^{2}}

\frac{d}{d x} (x^{2} + 1) = 2 x

\frac{d}{d x} (x - 9) = 1

= \frac{2 x ( x - 9 ) - 1 \cdot ( x ^{2} + 1 )}{( x - 9 ) ^{2}}

Vereinfache

\frac{2 x ( x - 9 ) - 1 \cdot ( x ^{2} + 1 )}{( x - 9 ) ^{2}} : \frac{x ^{2} - 18 x - 1}{( x - 9 ) ^{2}}

= \frac{x ^{2} - 18 x - 1}{( x - 9 ) ^{2}}

Graph

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