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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

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

\int \frac{1}{7 x lo g _{3} ( x )} d x

\frac{\partial}{\partial x} (y cos (x lo g_{e} (y)))

\frac{d y}{d t} = - 3 (y - 5)

x \to \infty lim (\frac{( \frac{x + 1}{x ^{3} + 2} )}{( \frac{x}{x ^{3}} )})

x \to 5 + lim (\frac{8}{x - 5})