derivative of 1/(5x^4-5/(2x))

Lösung

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

- \frac{4}{5 x ^{5}} + \frac{5}{2 x ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (\frac{5}{2 x}) = - \frac{5}{2 x ^{2}}

= - \frac{4}{5 x ^{5}} - (- \frac{5}{2 x ^{2}})

Vereinfache

= - \frac{4}{5 x ^{5}} + \frac{5}{2 x ^{2}}

t an g e n t f (x) = 6 x^{2}, (2, 24)

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