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Beliebt Rechnen >

derivative f(x)=(5x)/(7x^2+1)

Lösung

ableitung von

f (x) = \frac{5 x}{7 x ^{2} + 1}

Lösung

\frac{5 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 x}{7 x ^{2} + 1})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{x}{7 x ^{2} + 1})

Wende die Quotientenregel an:

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

= 5 \cdot \frac{\frac{d x}{d x} ( 7 x ^{2} + 1 ) - \frac{d}{d x} ( 7 x ^{2} + 1 ) x}{( 7 x ^{2} + 1 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (7 x^{2} + 1) = 14 x

= 5 \cdot \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}}

Vereinfache

5 \cdot \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}} : \frac{5 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

= \frac{5 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

Graph

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