derivative of (x^2-4^{1/3})

Lösung

\frac{d}{d x} ((x^{2} - 4)^{\frac{1}{3}})

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

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 4)^{\frac{1}{3}})

Wende die Kettenregel an:

\frac{1}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} - 4)

= \frac{1}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} - 4)

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

= \frac{1}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} \cdot 2 x

Vereinfache

\frac{1}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} \cdot 2 x : \frac{2 x}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}}

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

a re a x = - 2, x = 1, y = 2 x^{2} + 4, y = 0

\int x^{3} cos (n x) d x

d er i v a t i v e f (x) = r + 9 r

x \to - 7 lim (\frac{x}{x - 2})

s l o p e e^{x} + 1