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

Lösung

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

x^{2} - \frac{3 x e ^{x}}{y ^{4}}

Schritte zur Lösung

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

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

\frac{\partial}{\partial y} (\frac{x e ^{x}}{y ^{3}}) = - \frac{3 x e ^{x}}{y ^{4}}

= x^{2} - \frac{3 x e ^{x}}{y ^{4}}

a re a 2 x^{2} - 2 x - 6, - 2, 2

\int_{0}^{5} 46216.8 x d x

\int \frac{sin ( x )}{2 x} d x

d er i v a t i v e f (x) = 5 x sin (x)

\int_{0}^{π} cos (2 x) d x