derivative of 4/(x^4+1/x+2)

Lösung

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

- \frac{16}{x ^{5}} - \frac{1}{x ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{4}{x ^{4}}) = - \frac{16}{x ^{5}}

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

\frac{d}{d x} (2) = 0

= - \frac{16}{x ^{5}} - \frac{1}{x ^{2}} + 0

Vereinfache

= - \frac{16}{x ^{5}} - \frac{1}{x ^{2}}

x \to 0 lim ((1 + sin (3 x))^{\frac{1}{x}})

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