What is (\partial)/(\partial y)(e^{-x}sin(yz)) ?

The answer to (\partial)/(\partial y)(e^{-x}sin(yz)) is e^{-x}cos(yz)z

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(\partial)/(\partial y)(e^{-x}sin(yz))

\frac{\partial}{\partial y} (e^{- x} sin (yz))

e^{- x} cos (yz) z

Solution steps

\frac{\partial}{\partial y} (e^{- x} sin (yz))

Treat

x, z

as constants

Take the constant out:

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

= e^{- x} \frac{\partial}{\partial y} (sin (yz))

Apply the chain rule:

cos (yz) \frac{\partial}{\partial y} (yz)

= cos (yz) \frac{\partial}{\partial y} (yz)

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

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

What is (\partial)/(\partial y)(e^{-x}sin(yz)) ?
The answer to (\partial)/(\partial y)(e^{-x}sin(yz)) is e^{-x}cos(yz)z