(\partial)/(\partial y)(6x^{1/3}y^{2/3})

Lösung

\frac{\partial}{\partial y} (6 x^{\frac{1}{3}} y^{\frac{2}{3}})

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

Schritte zur Lösung

\frac{\partial}{\partial y} (6 x^{\frac{1}{3}} y^{\frac{2}{3}})

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 6 x^{\frac{1}{3}} \frac{2}{3} y^{\frac{2}{3} - 1}

Vereinfache

6 x^{\frac{1}{3}} \frac{2}{3} y^{\frac{2}{3} - 1} : \frac{4 x ^{\frac{1}{3}}}{y ^{\frac{1}{3}}}

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

\frac{\partial}{\partial x} (\frac{4 x}{( y + 2 z ) ^{3}})

x \to 0 lim (\frac{1}{x} sin (x))

\int_{0}^{3 π} ∣ sin (x) ∣ d x

\frac{d}{d x} (\frac{2 x}{x - 3})

d er i v a t i v e f (x) = \frac{3 + x}{1 - 3 x}