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Beliebt Rechnen >

derivative (x^4+2x^2)/(x^2)

Lösung

ableitung von

\frac{x ^{4} + 2 x ^{2}}{x ^{2}}

Lösung

2 x

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{4} + 2 x ^{2}}{x ^{2}})

Vereinfache

\frac{x ^{4} + 2 x ^{2}}{x ^{2}} : x^{2} + 2

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (2) = 0

= 2 x + 0

Vereinfache

= 2 x

Graph

Beliebte Beispiele

integral of e^x(x^2-5x)

\int e^{x} (x^{2} - 5 x) d x

(dy)/(dx)=(x^3)/(y^2)

\frac{d y}{d x} = \frac{x ^{3}}{y ^{2}}

integral of (1-cos(2x))^2

\int (1 - cos (2 x))^{2} d x

(d^3)/(dx^3)(1/(sqrt(x)))

\frac{d ^{3}}{d x ^{3}} (\frac{1}{x})

integral of (5x^2+6+7/(x^2+1))

\int (5 x^{2} + 6 + \frac{7}{x ^{2} + 1}) d x