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

The answer to (\partial)/(\partial y)(x^2cos(xy)) is -x^3sin(xy)

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(\partial)/(\partial y)(x^2cos(xy))

\frac{\partial}{\partial y} (x^{2} cos (x y))

- x^{3} sin (x y)

Solution steps

\frac{\partial}{\partial y} (x^{2} cos (x y))

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x^{2} (- sin (x y) x)

Simplify

x^{2} (- sin (x y) x) : - x^{3} sin (x y)

= - x^{3} sin (x y)

What is (\partial)/(\partial y)(x^2cos(xy)) ?
The answer to (\partial)/(\partial y)(x^2cos(xy)) is -x^3sin(xy)