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Beliebt Rechnen >

derivative of (5-x/x)

Lösung

\frac{d}{d x} (\frac{5 - x}{x})

Lösung

- \frac{5}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 - x}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 5 - x ) x - \frac{d x}{d x} ( 5 - x )}{x ^{2}}

\frac{d}{d x} (5 - x) = - 1

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

= \frac{( - 1 ) x - 1 \cdot ( 5 - x )}{x ^{2}}

Vereinfache

\frac{( - 1 ) x - 1 \cdot ( 5 - x )}{x ^{2}} : - \frac{5}{x ^{2}}

= - \frac{5}{x ^{2}}

Graph

Beliebte Beispiele

integral of x^3-1/(x^2)-x^{2/3}

\int x^{3} - \frac{1}{x ^{2}} - x^{\frac{2}{3}} d x

limit as x approaches infinity of 5x^2

x \to \infty lim (5 x^{2})

integral from 1 to 4 of x-1

\int_{1}^{4} x - 1 d x

derivative of (7^{10x+1})

\frac{d}{d x} ((7)^{10 x + 1})

derivative of x^2*x^{-1}

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