derivative \sqrt[5]{x^3}-8/x

Lösung

ableitung von

5 x^{3} - \frac{8}{x}

\frac{3 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}} + \frac{8}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (5 x^{3} - \frac{8}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x^{3}) - \frac{d}{d x} (\frac{8}{x})

\frac{d}{d x} (5 x^{3}) = \frac{3 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}}

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

= \frac{3 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}} - (- \frac{8}{x ^{2}})

Vereinfache

= \frac{3 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}} + \frac{8}{x ^{2}}

\int (- 6 sec (x) tan (x) - 7 sec^{2} (x)) d x

d er i v a t i v e 4 t

d er i v a t i v e ln (x^{2} + 5)

x \to 0 lim ((1 + \frac{3}{x ^{4}})^{x})

\frac{d}{d x} (x^{4} - 6 x - 9)