What is (\partial)/(\partial y)(xsin(xy)) ?

The answer to (\partial)/(\partial y)(xsin(xy)) is x^2cos(xy)

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(\partial)/(\partial y)(xsin(xy))

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

x^{2} cos (x y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= x cos (x y) x

Simplify

x cos (x y) x : x^{2} cos (x y)

= x^{2} cos (x y)

What is (\partial)/(\partial y)(xsin(xy)) ?
The answer to (\partial)/(\partial y)(xsin(xy)) is x^2cos(xy)