What is (\partial)/(\partial x)(xcos(y)-ysin(x)) ?

The answer to (\partial)/(\partial x)(xcos(y)-ysin(x)) is cos(y)-ycos(x)

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(\partial)/(\partial x)(xcos(y)-ysin(x))

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

cos (y) - y cos (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= cos (y) - y cos (x)

What is (\partial)/(\partial x)(xcos(y)-ysin(x)) ?
The answer to (\partial)/(\partial x)(xcos(y)-ysin(x)) is cos(y)-ycos(x)