derivative f(x)= x/(x-1)

Lösung

ableitung von

f (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}}

t an g e n t f (x) = 3 - 5 x + 2 x^{2}, (- 9, 210)

(x + y)^{2} d x + (2 x y + x^{2} - 9) d y = 0

x \to \infty lim (\frac{x}{2 x})

\frac{\partial}{\partial x} (\frac{x}{2 + y})

f (t) = cos (ln (t))