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Beliebt Rechnen >

derivative of (x+1/x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

\frac{1 \cdot x - 1 \cdot ( x + 1 )}{x ^{2}} : - \frac{1}{x ^{2}}

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

Graph

Beliebte Beispiele

limit as x approaches+2 of 2x

x \to + 2 lim (2 x)

integral of sin^4(3x)cos^3(3x)

\int sin^{4} (3 x) cos^{3} (3 x) d x

integral of (4x+3)^2

\int (4 x + 3)^{2} d x

limit as x approaches-3 of (x^2+1)/(2x)

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

derivative f(x)=4x^{-1/2}

d er i v a t i v e f (x) = 4 x^{- \frac{1}{2}}