Find : ∂z/∂x

$\displaystyle

z = 3x\sqrt{y} - xcos(xy)

$

My solution:

$\displaystyle Let K = xcos(xy)$

$\displaystyle Let u = x , v = cos(xy)$

∂u/∂x = 1

∂v/∂x = $\displaystyle -ysin(xy)$

Product rule:

∂K/∂x = v(∂u/∂x) + u(∂v/∂x) = $\displaystyle cos(xy) - xysin(xy)$

∂z/∂x = $\displaystyle 3\sqrt{y} -cos(xy) -xysin(xy)

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