(\partial)/(\partial y)(x^{0.5}y^{0.5})

Lösung

\frac{\partial}{\partial y} (x^{0.5} y^{0.5})

\frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{0.5} y^{0.5})

Behandle

x

als Konstante

Entferne die Konstante:

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

= x^{0.5} \frac{\partial}{\partial y} (y^{0.5})

Wende die Potenzregel an:

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

= x^{0.5} \cdot 0.5 y^{0.5 - 1}

Vereinfache

x^{\frac{1}{2}} \cdot 0.5 y^{0.5 - 1} : \frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

= \frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

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

\int \frac{x ^{3}}{5 x ^{4} - 1} d x

\int (3 x + 4)^{3} d x

d er i v a t i v e \frac{1}{x ^{2} - 1}

\frac{d}{d x} (1 + \frac{1}{x})