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Beliebt Rechnen >

derivative of-x+1/x+1

Lösung

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

Lösung

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

Schritte zur Lösung

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

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}{d x} (1)

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

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

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

= - 1 - \frac{1}{x ^{2}} + 0

Vereinfache

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

Graph

Beliebte Beispiele

sum from n=1 to infinity of (sin(1))^n

n = 1 \sum \infty (sin (1))^{n}

derivative y=x^3-4x+4

d er i v a t i v e y = x^{3} - 4 x + 4

integral of y/(y^2)

\int \frac{y}{y ^{2}} d y

integral of (x^2+7x)cos(x)

\int (x^{2} + 7 x) cos (x) d x

derivative of cos^2(sqrt(x))

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