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Beliebt Rechnen >

derivative of 460(1+x/(x^2+80))

Lösung

\frac{d}{d x} (460 (1 + \frac{x}{x ^{2} + 80}))

Lösung

\frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (460 (1 + \frac{x}{x ^{2} + 80}))

Entferne die Konstante:

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

= 460 \frac{d}{d x} (1 + \frac{x}{x ^{2} + 80})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 460 (\frac{d}{d x} (1) + \frac{d}{d x} (\frac{x}{x ^{2} + 80}))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (\frac{x}{x ^{2} + 80}) = \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}}

= 460 (0 + \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}})

Vereinfache

460 (0 + \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}}) : \frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}

= \frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}

Graph

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