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)

\)

\(\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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