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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{60}{0.01 x ^{2} + 1})

\frac{d}{d x} (- \frac{9}{x})

(arctan (\frac{1}{x}))^{^{'}}

\frac{\partial}{\partial x} (x^{4 c o s (x)})

\int \frac{4 + x ^{2}}{x ^{3}} d x