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Beliebt Rechnen >

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

Lösung

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

Lösung

e^{y + 2 x^{2}} + 4 e^{y + 2 x^{2}} x (x - y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

\frac{\partial}{\partial x} (e^{y + 2 x^{2}}) = e^{y + 2 x^{2}} \cdot 4 x

= 1 \cdot e^{y + 2 x^{2}} + e^{y + 2 x^{2}} \cdot 4 x (x - y)

Vereinfache

= e^{y + 2 x^{2}} + 4 e^{y + 2 x^{2}} x (x - y)

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