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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

x^{\frac{1}{2}} \frac{1}{2} y^{\frac{1}{2} - 1} : \frac{x ^{\frac{1}{2}}}{2 y ^{\frac{1}{2}}}

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

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

d er i v a t i v e 2 x + 4

x \to 0 lim (x^{2} + 1)

\frac{\partial}{\partial x} (e^{y s i n (x)})

\frac{d}{d x} (4 9 - x)