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

The answer to (\partial)/(\partial y)(xsin(x)+ysin(y)) is ycos(y)+sin(y)

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

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

y cos (y) + sin (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= y cos (y) + sin (y)

y^{^{''}} = k^{2} y

\frac{d}{d x} (\frac{1 - x}{2 + x})

\frac{d}{d x} ((x + e^{2 x})^{3})

\int (sec (x))^{3} d x

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