What is (\partial)/(\partial y)(cos(x)cos(y)+2x) ?

The answer to (\partial)/(\partial y)(cos(x)cos(y)+2x) is -cos(x)sin(y)

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(\partial)/(\partial y)(cos(x)cos(y)+2x)

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

- cos (x) sin (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial y} (2 x) = 0

= - cos (x) sin (y) + 0

Simplify

= - cos (x) sin (y)

What is (\partial)/(\partial y)(cos(x)cos(y)+2x) ?
The answer to (\partial)/(\partial y)(cos(x)cos(y)+2x) is -cos(x)sin(y)