derivative of 6\sqrt[3]{x^2}

Lösung

\frac{d}{d x} (6 3 x^{2})

\frac{4}{x ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} (6 3 x^{2})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (3 x^{2})

Wende die Kettenregel an:

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

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

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

= 6 \cdot \frac{1}{3 ( x ^{2} ) ^{\frac{2}{3}}} \cdot 2 x

Vereinfache

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

= \frac{4}{x ^{\frac{1}{3}}}

x \to \frac{1}{8} lim (\frac{1}{x} - x^{- 1})

\int x^{2} (x + 2) d x

\int_{0}^{1} x e^{8 x} d x

\int \frac{1}{x 4 - 9 ln ^{2} ( x )} d x

t an g e n t f (x) = sin (2 x), at x = - \frac{π}{3}