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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d y}{d t} = 5 - y

\frac{d}{d x} (\frac{500}{x})

\frac{\partial}{\partial x} (\frac{4 x - 5 y}{4 x + 5 y})

(x^{2} + y^{2} + x) d x + y d y = 0

d er i v a t i v e f (x) = 9 x + 8