(\partial)/(\partial y)(x^2y+xy^3)

Lösung

\frac{\partial}{\partial y} (x^{2} y + x y^{3})

x^{2} + 3 x y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2} y + x y^{3})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{2} y) + \frac{\partial}{\partial y} (x y^{3})

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

\frac{\partial}{\partial y} (x y^{3}) = 3 x y^{2}

= x^{2} + 3 x y^{2}

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

\frac{d x}{d t} = \frac{457.8 - 7 x}{2180}

d er i v a t i v e (1 - e^{x^{3}})^{5}

x \to 1 - lim (x^{2} - 2)

t an g e n t y = \frac{x ^{2} - 1}{x ^{2} + x + 1}, (1, 0)