derivative of x^2-8/(x^3)

Lösung

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

2 x + \frac{24}{x ^{4}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (\frac{8}{x ^{3}}) = - \frac{24}{x ^{4}}

= 2 x - (- \frac{24}{x ^{4}})

Vereinfache

= 2 x + \frac{24}{x ^{4}}