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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{3}{s ^{4}}

s l o p e x^{2} + 2

\int 1 - 2 cos (x) + cos^{2} (x) d x

\int \frac{e ^{\frac{6}{x}}}{x ^{2}} d x

\int \frac{1}{s} d s