derivative of \sqrt[3]{x^8}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{3 ( x ^{8} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{8})

= \frac{1}{3 ( x ^{8} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{1}{3 ( x ^{8} ) ^{\frac{2}{3}}} \cdot 8 x^{7}

Vereinfache

\frac{1}{3 ( x ^{8} ) ^{\frac{2}{3}}} \cdot 8 x^{7} : \frac{8 x ^{\frac{5}{3}}}{3}

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

\int e^{2 x} 1 + e^{2 x} d x

\frac{\partial}{\partial x} (\frac{6 y}{( x + y ) ^{2}})

x \to - \infty lim (2 - x)

\int_{1}^{5} \frac{x}{2 x + 1} d x

\int π (2 x - 4)^{2} d x