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Beliebt Rechnen >

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

Lösung

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

Lösung

\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}}}

Beliebte Beispiele

d/(dt)((cos(t))/(sin(t)))

\frac{d}{d t} (\frac{cos ( t )}{sin ( t )})

derivative of xarctan(2x)

\frac{d}{d x} (x arctan (2 x))

limit as x approaches 0-of xcsc(x)

x \to 0 - lim (x csc (x))

(d^2)/(dx^2)(cos(-2x))

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

derivative of cos(x^2+pi)

\frac{d}{d x} (cos (x^{2} + π))