derivative y= x/(x-1)

Lösung

ableitung von

y = \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}}

\int_{0}^{1} 1 - x^{\frac{2}{5}} d x

a re a f (x) = x^{3} - x^{2} - x, g (x) = x

(2 x y^{3} - 3 x^{2} y^{2}) d x + (x y^{3} + 2 x^{2} y^{2}) d y = 0

\frac{d y}{d t} = 0.04 y (400 - y)

\int x - 1 d x