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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{( 8 x ^{2} + 3 x - 6 )}{( x ^{2} - 4 ) ( x + 2 )} d x

\frac{\partial}{\partial y} (2 arctan (\frac{x}{y}))

\frac{d y}{d x} = 4 y^{2} x

\int cot (10 x) d x

\int \frac{x ^{2} + 24}{x ( x - 2 ) ^{3}} d x