(\partial)/(\partial y)(sqrt(x^2y-xy^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

4 y^{^{''}} - 12 y^{^{'}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 5

n \to \infty lim (\frac{ln ( n )}{ln ( 2 n )})

\int \frac{1}{( x - 3 ) ( x + 4 )} d x

x \to 0 lim (x^{0})

d er i v a t i v e f (x) = \frac{1}{x - 3}