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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 0 lim (\frac{4}{x} - \frac{4}{e ^{x} - 1})

\frac{\partial}{\partial x} ((6 x + 3 y) ey)

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

s l o p e (1, 6), (0.5, 8)

x \to 0 lim ((1 - 2 x)^{\frac{1}{2}})