What is (\partial)/(\partial y)(x^2+sin(xy)) ?

The answer to (\partial)/(\partial y)(x^2+sin(xy)) is xcos(xy)

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(\partial)/(\partial y)(x^2+sin(xy))

\frac{\partial}{\partial y} (x^{2} + sin (x y))

x cos (x y)

Solution steps

\frac{\partial}{\partial y} (x^{2} + sin (x y))

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{2}) + \frac{\partial}{\partial y} (sin (x y))

\frac{\partial}{\partial y} (x^{2}) = 0

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

= 0 + cos (x y) x

Simplify

= x cos (x y)

What is (\partial)/(\partial y)(x^2+sin(xy)) ?
The answer to (\partial)/(\partial y)(x^2+sin(xy)) is xcos(xy)