(\partial)/(\partial x)(6e^ysin(4x)+3y-2xy)

Lösung

\frac{\partial}{\partial x} (6 e^{y} sin (4 x) + 3 y - 2 x y)

24 e^{y} cos (4 x) - 2 y

Schritte zur Lösung

\frac{\partial}{\partial x} (6 e^{y} sin (4 x) + 3 y - 2 x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (6 e^{y} sin (4 x)) + \frac{\partial}{\partial x} (3 y) - \frac{\partial}{\partial x} (2 x y)

\frac{\partial}{\partial x} (6 e^{y} sin (4 x)) = 24 e^{y} cos (4 x)

\frac{\partial}{\partial x} (3 y) = 0

\frac{\partial}{\partial x} (2 x y) = 2 y

= 24 e^{y} cos (4 x) + 0 - 2 y

Vereinfache

= 24 e^{y} cos (4 x) - 2 y

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