derivative 1/x+1/(x-1)+1/(x-2)

Lösung

ableitung von

\frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2}

\frac{- 3 x ^{4} + 12 x ^{3} - 18 x ^{2} + 12 x - 4}{x ^{2} ( x - 1 ) ^{2} ( x - 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

Vereinfache

- \frac{1}{x ^{2}} - \frac{1}{( x - 1 ) ^{2}} - \frac{1}{( x - 2 ) ^{2}} : \frac{- 3 x ^{4} + 12 x ^{3} - 18 x ^{2} + 12 x - 4}{x ^{2} ( x - 1 ) ^{2} ( x - 2 ) ^{2}}

= \frac{- 3 x ^{4} + 12 x ^{3} - 18 x ^{2} + 12 x - 4}{x ^{2} ( x - 1 ) ^{2} ( x - 2 ) ^{2}}

\int x^{2} \cdot sin (x^{3}) d x

n = 1 \sum \infty 15 (\frac{1}{100})^{n}

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

d er i v a t i v e x (x^{5} + 2)

x \to 0 lim ((2 x^{2} + x)^{x})