derivative-1/x-1/(x^2)+1/(x^3)

Lösung

ableitung von

- \frac{1}{x} - \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

\frac{1}{x ^{2}} + \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

Schritte zur Lösung

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

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

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

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

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

Vereinfache

= \frac{1}{x ^{2}} + \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

in v erse l a pl a ce \frac{s + 1}{s ( s + 2 ) ( s + 4 )}

in v erse l a pl a ce \frac{1}{s ^{2} ( s - 3 ) ^{2}}

\int \frac{1}{t - 2} d t

\int \frac{3 x ^{3}}{4 - x ^{2}} d x

\int \frac{1}{x ^{n}} d x