derivative x/(1-\frac{1){x^2}}

Lösung

ableitung von

\frac{x}{1 - \frac{1}{x ^{2}}}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

a re a \frac{7}{x}, x = 1, x = 41

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

x \to + 3 lim (\frac{8}{x - 3})

\int_{0}^{\frac{π}{4}} 6 tan^{3} (x) d x