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

Lösung

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

2 y x - y^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 2 y x - y^{2}

t an g e n t f (x) = 2 x + 3, (3, 3)

d er i v a t i v e y = 6 ln (x) - x^{3} + 2 3 x

x \to \infty lim (arctan (8 x))

\int_{1}^{\infty} \frac{9}{x ^{4}} d x

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