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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 \cdot \frac{1}{1 - x} \cdot \frac{1}{( 1 - x ) ^{2}} : \frac{2}{( 1 - x ) ^{3}}

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

t an g e n t \frac{8}{x}

\frac{d x}{d t} + 5 x = 50

\frac{d}{d x} (\frac{7 e ^{x}}{2 e ^{x} + 1})

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

d er i v a t i v e \frac{x ^{3} - x}{1 + x ^{2}}