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Beliebt Rechnen >

derivative x-1/x

Lösung

ableitung von

x - \frac{1}{x}

Lösung

1 + \frac{1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x - \frac{1}{x})

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

= 1 + \frac{1}{x ^{2}}

Graph

Beliebte Beispiele

derivative of 6xln(x)

\frac{d}{d x} (6 x ln (x))

tangent y=4(x-1x)4,\at x=2

t an g e n t y = 4 (x - 1 x) 4, at x = 2

limit as x approaches 7 of |x-7|

x \to 7 lim (∣ x - 7 ∣)

derivative h(x)=sqrt(x)

d er i v a t i v e h (x) = x

limit as x approaches-5 of (x^2-4)/(5-x)

x \to - 5 lim (\frac{x ^{2} - 4}{5 - x})