What is (\partial)/(\partial y)(xcos(yz)) ?

The answer to (\partial)/(\partial y)(xcos(yz)) is -xzsin(yz)

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(\partial)/(\partial y)(xcos(yz))

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

- x z sin (yz)

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

- sin (yz) \frac{\partial}{\partial y} (yz)

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

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

= x (- sin (yz) z)

Simplify

= - x z sin (yz)

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\frac{\partial}{\partial y} (e^{2 x + 5 y})

What is (\partial)/(\partial y)(xcos(yz)) ?
The answer to (\partial)/(\partial y)(xcos(yz)) is -xzsin(yz)