derivative f(x)= 5/(x^3)-4/(x^2)+1/x

Lösung

ableitung von

f (x) = \frac{5}{x ^{3}} - \frac{4}{x ^{2}} + \frac{1}{x}

- \frac{15}{x ^{4}} + \frac{8}{x ^{3}} - \frac{1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{x ^{3}} - \frac{4}{x ^{2}} + \frac{1}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{5}{x ^{3}}) - \frac{d}{d x} (\frac{4}{x ^{2}}) + \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (\frac{5}{x ^{3}}) = - \frac{15}{x ^{4}}

\frac{d}{d x} (\frac{4}{x ^{2}}) = - \frac{8}{x ^{3}}

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

= - \frac{15}{x ^{4}} - (- \frac{8}{x ^{3}}) - \frac{1}{x ^{2}}

Vereinfache

= - \frac{15}{x ^{4}} + \frac{8}{x ^{3}} - \frac{1}{x ^{2}}

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