derivative of 3/(x^3-1/(x^4))

Lösung

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

- \frac{9}{x ^{4}} + \frac{4}{x ^{5}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{3}{x ^{3}}) = - \frac{9}{x ^{4}}

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

= - \frac{9}{x ^{4}} - (- \frac{4}{x ^{5}})

Vereinfache

= - \frac{9}{x ^{4}} + \frac{4}{x ^{5}}

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

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