(\partial)/(\partial y)(xe^{xy}+y^2sin(xy))

Lösung

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

x^{2} e^{x y} + 2 y sin (x y) + cos (x y) x y^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= x^{2} e^{x y} + 2 y sin (x y) + cos (x y) x y^{2}

\frac{\partial}{\partial x} (ln (x^{7} + y^{4}))

in v erse l a pl a ce \frac{2}{s ^{3}}

\int_{0}^{\frac{π}{2}} - 2 cos^{5} (x) d x

d er i v a t i v e (6 z + e^{- z^{2}})^{3}

\frac{\partial}{\partial x} (2 y sin (10 x - y))