(\partial)/(\partial x)(cos(xy)e^{x^2})

Lösung

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

- e^{x^{2}} y sin (x y) + 2 e^{x^{2}} x cos (x y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = cos (x y), g = e^{x^{2}}

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

\frac{\partial}{\partial x} (cos (x y)) = - sin (x y) y

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

= (- sin (x y) y) e^{x^{2}} + e^{x^{2}} \cdot 2 x cos (x y)

Vereinfache

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

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