derivative f(x)= 4/x-2/(x^3)+1/(x^4)

Lösung

ableitung von

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

- \frac{4}{x ^{2}} + \frac{6}{x ^{4}} - \frac{4}{x ^{5}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (\frac{2}{x ^{3}}) = - \frac{6}{x ^{4}}

\frac{d}{d x} (\frac{1}{x ^{4}}) = - \frac{4}{x ^{5}}

= - \frac{4}{x ^{2}} - (- \frac{6}{x ^{4}}) - \frac{4}{x ^{5}}

Vereinfache

= - \frac{4}{x ^{2}} + \frac{6}{x ^{4}} - \frac{4}{x ^{5}}