What is (\partial)/(\partial y)(cos(x+y+z)) ?

The answer to (\partial)/(\partial y)(cos(x+y+z)) is -sin(x+y+z)

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(\partial)/(\partial y)(cos(x+y+z))

\frac{\partial}{\partial y} (cos (x + y + z))

- sin (x + y + z)

Solution steps

\frac{\partial}{\partial y} (cos (x + y + z))

Treat

x, z

as constants

Apply the chain rule:

- sin (x + y + z) \frac{\partial}{\partial y} (x + y + z)

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

\frac{\partial}{\partial y} (x + y + z) = 1

= - sin (x + y + z) \cdot 1

Simplify

= - sin (x + y + z)

What is (\partial)/(\partial y)(cos(x+y+z)) ?
The answer to (\partial)/(\partial y)(cos(x+y+z)) is -sin(x+y+z)