(\partial)/(\partial y)(ycos(y-2x))

Lösung

\frac{\partial}{\partial y} (y cos (y - 2 x))

cos (y - 2 x) - y sin (y - 2 x)

Schritte zur Lösung

\frac{\partial}{\partial y} (y cos (y - 2 x))

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = y, g = cos (y - 2 x)

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

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

\frac{\partial}{\partial y} (cos (y - 2 x)) = - sin (y - 2 x)

= 1 \cdot cos (y - 2 x) + (- sin (y - 2 x)) y

Vereinfache

= cos (y - 2 x) - y sin (y - 2 x)

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