derivative y= 6/(x^4)-4/(x^2)-3/x

Lösung

ableitung von

y = \frac{6}{x ^{4}} - \frac{4}{x ^{2}} - \frac{3}{x}

- \frac{24}{x ^{5}} + \frac{8}{x ^{3}} + \frac{3}{x ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{6}{x ^{4}}) = - \frac{24}{x ^{5}}

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

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

= - \frac{24}{x ^{5}} - (- \frac{8}{x ^{3}}) - (- \frac{3}{x ^{2}})

Vereinfache

= - \frac{24}{x ^{5}} + \frac{8}{x ^{3}} + \frac{3}{x ^{2}}

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