Find partial z/partial x & partial z / partial y from the given functions (i) z=log (xy+2)(xy^2-2y^2) (ii) z=[e^xy sin(2y)] [x^2sin (xy)]?

i)
I have assume∂ log( base e) = ln

Because there is no parenthesis, I assume the log applies only to (xy+2)

∂z/∂x = [x/(xy+2) ] (xy^2-2y^2) + log (xy+2) (y^2)
∂z/∂x = (x^3y^2-2y^2x) /(xy+2) + y^2 log(xy+2)
∂z/∂x = y^2x (x^2-2) /(xy+2) + y^2 log(xy+2)

∂z/∂y = [y/(xy+2)] ( xy^2-2y^2) + log (xy+2) (2xy-4y)
∂z/∂y = (xy^3-2y^3) /(xy+2) + log(xy+2) (2xy-4y)

ii)
z = e^(xy) sin(2y) x^2 sin(xy)
∂z/∂x = ∂/∂x (e^(xy) ) sin(2y) x^2 sin(xy) + ∂/∂x (x^2) e^(xy) sin(2y) sin(xy) + ∂/∂x ( sin(xy)) e^(xy) sin(2y) x^2
∂z/∂x = y e^(xy) sin(2y) x^2 sin(xy) + 2x e^(xy) sin(2y) sin(xy) + y cos(xy) e^(xy) sin(2y) x^2

∂z/∂y = ∂/∂y( e^(xy) ) sin(2y) x^2 sin(xy) + ∂/∂y (sin(2y) ) e^(xy) x^2 sin(xy) + ∂/∂y ( sin(xy) ) e^(xy) sin(2y) x^2
∂z/∂y = ye^(xy) sin(2y) x^2 sin (xy) + 2 cos(2y) e^(xy) x^2 sin(xy) + x cos(xy) e^(xy) sin(2y) x^2