(\partial)/(\partial x)(x/(x^2-2x+1))

Lösung

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

- \frac{x + 1}{( x - 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

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

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

s l o p e in t erce pt (- 2, 5.5), (0, 5.5)

\int \frac{5 x ^{2} + x - 34}{( x + 1 ) ^{2} ( x - 4 )} d x

d er i v a t i v e \frac{x}{2}

\frac{d}{d x} (\frac{2 x + 7}{2 x})