(\partial)/(\partial y)(xye^{x+y})

Lösung

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

x (e^{x + y} + e^{x + y} y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = e^{x + y}

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

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

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

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

Vereinfache

= x (e^{x + y} + e^{x + y} y)

\int (sin (2 x) - sin (3 x))^{2} d x

t an g e n t f (x) = \frac{5}{x}, (3, \frac{5}{3})

\frac{\partial}{\partial t} (e^{- 2 x} cos (9 π t))

t a y l or \frac{1}{2} arctan (2 x)

n = 1 \sum \infty 3 e^{- 4 n}