derivative of x/((x-1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d r} (\frac{1}{2 r} + \frac{1}{3 r ^{\frac{2}{3}}})

\frac{d}{d x} (f (h, x) (g (h, x) (h (x))))

d er i v a t i v e (x + 1)^{2}

\frac{d y}{d x} = \frac{x ^{3} + 2 y ^{3}}{x y ^{2}}

in v erse l a pl a ce e^{- π s} \frac{2}{s ^{3}}