derivative of (x^{10}/(20)+1/(16x^8))

Lösung

\frac{d}{d x} (\frac{x ^{10}}{20} + \frac{1}{16 x ^{8}})

\frac{x ^{9}}{2} - \frac{1}{2 x ^{9}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{10}}{20} + \frac{1}{16 x ^{8}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{10}}{20}) + \frac{d}{d x} (\frac{1}{16 x ^{8}})

\frac{d}{d x} (\frac{x ^{10}}{20}) = \frac{x ^{9}}{2}

\frac{d}{d x} (\frac{1}{16 x ^{8}}) = - \frac{1}{2 x ^{9}}

= \frac{x ^{9}}{2} - \frac{1}{2 x ^{9}}

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