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

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

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

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

cos (y) + sin (x)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= cos (y) + sin (x)

x \to 5 - lim (3)

y^{^{''}} = x^{2} - 1

5^{x}

\int 3 x - 4 d x

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

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