(\partial)/(\partial x)((x+y)*e^{x+2y})

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x + y, g = e^{x + 2 y}

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

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

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

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

Vereinfache

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

a re a 4 - (x - 2)^{2}, 5 - (x - 4)^{2}, 2, 4

\int 4 cos^{2} (2 x) + 4 sin^{2} (2 x) d x

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

x \to - \infty lim (\frac{1}{4 x})

\frac{d}{d y} (x^{(1 + y)})