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

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

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

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

- x sin (y) - cos (x)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

sin (t + c)

\int cos^{4} (\frac{x}{5}) d x

\int \frac{x + 3}{x ^{2} 2 x + 3} d x

y^{^{'}} = \frac{x ^{4} y ^{4} - 2 x ^{4}}{y ^{3}}

x \to \infty lim (3 x^{2} + 1)

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