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Beliebt Rechnen >

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

Lösung

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

Lösung

2 x - 1

Schritte zur Lösung

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

Vereinfache

\frac{x ^{3} + x ^{2} - x + 2}{x + 2} : x^{2} - x + 1

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 2 x - 1 + 0

Vereinfache

= 2 x - 1

Graph

Beliebte Beispiele

limit as x approaches 0 of ((a^x-1))/x

x \to 0 lim (\frac{( a ^{x} - 1 )}{x})

integral from 1 to 5 of (x+1)^2

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

derivative (t^2+1)(t-1/t)

d er i v a t i v e (t^{2} + 1) (t - \frac{1}{t})

(\partial)/(\partial x)(2x^y)

\frac{\partial}{\partial x} (2 x^{y})

\frac{d x}{d t} = x - 11