derivative of (2x-3/(x-1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 0 lim (e^{- 2 f (x)})

\frac{\partial}{\partial x} (\frac{1}{1 - y})

t \to 0 lim (\frac{sin ( - 4 t )}{t})

l a pl a ce t r an s f or m h

x \to 1 lim (\frac{( x + 1 ) ^{2} - 1}{x})