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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

y^{^{'}} + 8 y = 1, y (0) = 1

\frac{d}{d x} (\frac{x - 5}{4 x ^{2} e ^{x}})

x \to 0 lim (x^{4} cos (\frac{1}{x}))

(e^{- 2 t})^{^{'}}

\int \frac{- 6 x ^{4} + 6}{x ^{2} + 1} d x