(\partial)/(\partial y)(6e^{yz}cos(xyz))

Lösung

\frac{\partial}{\partial y} (6 e^{yz} cos (x yz))

6 (e^{yz} z cos (yz x) - e^{yz} z x sin (yz x))

Schritte zur Lösung

\frac{\partial}{\partial y} (6 e^{yz} cos (x yz))

Behandle

z, x

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{\partial}{\partial y} (e^{yz} cos (x yz))

Wende die Produktregel an:

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

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

= 6 (\frac{\partial}{\partial y} (e^{yz}) cos (x yz) + \frac{\partial}{\partial y} (cos (x yz)) e^{yz})

\frac{\partial}{\partial y} (e^{yz}) = e^{yz} z

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

= 6 (e^{yz} z cos (x yz) + (- sin (x yz) z x) e^{yz})

Vereinfache

= 6 (e^{yz} z cos (yz x) - e^{yz} z x sin (yz x))