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

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

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

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

- sin (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - sin (y)

Simplify

= - sin (y)

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