(\partial)/(\partial y)(e^x(x-y)^2)

Lösung

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

- 2 e^{x} (x - y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (x - y) = - 1

= e^{x} \cdot 2 (x - y) (- 1)

Vereinfache

= - 2 e^{x} (x - y)

\int (cos (x) + 3^{x}) d x

x \to 0 lim (\frac{( 2 - x ) ^{2} + 1}{x})

\int_{- \infty}^{\infty} 15 x e^{- x^{2}} d x

\frac{\partial}{\partial z} (e^{x} cos (y))

\frac{\partial}{\partial x} (x^{2} + 3 x y + y - 1)