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Beliebt Rechnen >

derivative f(x)=(1-x)/x

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of xsin(xcos(x))

\frac{d}{d x} (x sin (x) cos (x))

integral of x^{10}

\int x^{10} d x

integral from 0 to 2 of e^{-3x}

\int_{0}^{2} e^{- 3 x} d x

y^{''}+y^'-6y=6t-7-(20te^{2t}+14e^{2t})

y^{^{''}} + y^{^{'}} - 6 y = 6 t - 7 - (20 t e^{2 t} + 14 e^{2 t})

tangent f(x)=x^6,\at x=2

t an g e n t f (x) = x^{6}, at x = 2