(\partial)/(\partial z)(\sqrt[3]{xyz})

Lösung

\frac{\partial}{\partial z} (3 x yz)

\frac{x ^{\frac{1}{3}} y ^{\frac{1}{3}}}{3 z ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{\partial}{\partial z} (3 x yz)

Behandle

x, y

als Konstanten

Wende die Kettenregel an:

\frac{1}{3 ( x yz ) ^{\frac{2}{3}}} \frac{\partial}{\partial z} (x yz)

= \frac{1}{3 ( x yz ) ^{\frac{2}{3}}} \frac{\partial}{\partial z} (x yz)

\frac{\partial}{\partial z} (x yz) = x y

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

Vereinfache

\frac{1}{3 ( x yz ) ^{\frac{2}{3}}} x y : \frac{x ^{\frac{1}{3}} y ^{\frac{1}{3}}}{3 z ^{\frac{2}{3}}}

= \frac{x ^{\frac{1}{3}} y ^{\frac{1}{3}}}{3 z ^{\frac{2}{3}}}

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

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

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

d er i v a t i v e \frac{1}{cos ( x )}

\int \frac{37}{x ^{3} - 125} d x