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Beliebt Rechnen >

derivative f(x)=2x+(x^2-x)/(x^3+x+1)

Lösung

ableitung von

f (x) = 2 x + \frac{x ^{2} - x}{x ^{3} + x + 1}

Lösung

2 + \frac{- x ^{4} + 2 x ^{3} + x ^{2} + 2 x - 1}{( x ^{3} + x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 x + \frac{x ^{2} - x}{x ^{3} + x + 1})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x) + \frac{d}{d x} (\frac{x ^{2} - x}{x ^{3} + x + 1})

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (\frac{x ^{2} - x}{x ^{3} + x + 1}) = \frac{- x ^{4} + 2 x ^{3} + x ^{2} + 2 x - 1}{( x ^{3} + x + 1 ) ^{2}}

= 2 + \frac{- x ^{4} + 2 x ^{3} + x ^{2} + 2 x - 1}{( x ^{3} + x + 1 ) ^{2}}

Graph

Beliebte Beispiele

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