What is (\partial)/(\partial y)(xsin(y)+ycos(x)) ?

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

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(\partial)/(\partial y)(xsin(y)+ycos(x))

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

x cos (y) + cos (x)

Solution steps

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

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

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

= x cos (y) + cos (x)

\int \frac{x ^{2} - 4}{x} d x

\frac{d}{d x} (x^{2} 2 x - 3)

x^{2} y^{^{'}} + \frac{4}{3} x y = - 4 cos (3 x) y^{- \frac{1}{2}}

x \to 1 + lim (\frac{1}{x ^{2} - 1})

y^{^{''}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

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