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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

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

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

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

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

Vereinfache

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

Beliebte Beispiele

laplacetransform t^2-2t

l a pl a ce t r an s f or m t^{2} - 2 t

derivative-7/(\sqrt[4]{x)}

d er i v a t i v e - \frac{7}{4 x}

integral of (x^4)/(8-x^5)

\int \frac{x ^{4}}{8 - x ^{5}} d x

(x+ye^{y/x})dx-xe^{y/x}dy=0

(x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

integral from-1 to 1 of e^y-y^2+6

\int_{- 1}^{1} e^{y} - y^{2} + 6 d y