What is (\partial)/(\partial x)(ycos(xy)) ?

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

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(\partial)/(\partial x)(ycos(xy))

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

- y^{2} sin (y x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y (- sin (x y) y)

Simplify

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

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

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