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Beliebt Rechnen >

derivative of ((1-x)/x)

Lösung

\frac{d}{d 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

y^{''}+6y^'+9y=t^{-2}e^{-3t}

y^{^{''}} + 6 y^{^{'}} + 9 y = t^{- 2} e^{- 3 t}

y^'= 3/((x+2)^2)

y^{^{'}} = \frac{3}{( x + 2 ) ^{2}}

derivative 7^{x+arccos(x)}

d er i v a t i v e 7^{x + a r c c o s (x)}

integral from pi/5 to infinity of 5/x

\int_{\frac{π}{5}}^{\infty} \frac{5}{x} d x

f^{^{'}} (x) = \frac{3}{x}