derivative (sqrt(x))/(x-1)

Lösung

ableitung von

\frac{x}{x - 1}

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

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

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

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

Vereinfache

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

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

\int_{0}^{1} (x^{2} - 8) e^{- x} d x

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

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

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

d er i v a t i v e y = 2