(\partial)/(\partial y)(1/(xy^2-x^2y))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{x}{3 + x ^{2}} d x

x y^{^{'}} - 2 y = x^{3}

a re a y = x - 1, y = 0, x = 9

d er i v a t i v e x - 2 3 x

h \to 1 lim (\frac{e ^{- h} - 1}{h})