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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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