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Beliebt Rechnen >

derivative of (1-2x/(1+2x))

Lösung

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

Lösung

- \frac{4}{( 1 + 2 x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( - 2 ) ( 1 + 2 x ) - 2 ( 1 - 2 x )}{( 1 + 2 x ) ^{2}} : - \frac{4}{( 1 + 2 x ) ^{2}}

= - \frac{4}{( 1 + 2 x ) ^{2}}

Graph

Beliebte Beispiele

limit as x approaches 1 of 2x+2

x \to 1 lim (2 x + 2)

(d^2)/(dx^2)(x^{3/2})

\frac{d ^{2}}{d x ^{2}} (x^{\frac{3}{2}})

integral of (-1)/(sqrt(x^2+16))

\int \frac{- 1}{x ^{2} + 16} d x

derivative of (x^2-3x/(2x+1))

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

inverselaplace s/(9s+81)

in v erse l a pl a ce \frac{s}{9 s + 81}