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

Lösung

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

2 e^{x y^{2}} x^{2} y

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= x e^{x y^{2}} \cdot 2 x y

Vereinfache

x e^{x y^{2}} \cdot 2 x y : 2 e^{x y^{2}} x^{2} y

= 2 e^{x y^{2}} x^{2} y

\int 3 w + 10 5 w^{3} d w

x \to - 1 - lim (- 4 x - 4 - 8)

y^{^{'}} + y = \frac{1 - x}{2 x ^{2}}

t an g e n t y^{6} + x^{3} = y^{2} + 12 x, (0, 1)

x \to - 1 lim (\frac{x}{0})