Finding The Derivative Of Trig Functions

I am struggling with implict differentiation if someone could help me. The question says: "Use implict differentiation to find dy/dx if y - sin(xy) = x^2"

Also this problem, "Find dy/dx if y = tan^-1(x-4)"

Thanks :)

1.) y - sin(xy) = x²

Differentiating implicitly:

y' - cos(xy)*(xy' + y) = 2x

y' - xy'*cos(xy) - y*cos(xy) = 2x

y' = (2x + y*cos(xy))/(1 - x*cos(xy))

2.) y = arctan(x - 4)

dy/dx = 1/[(x - 4)² + 1]

A) if y - sin(xy) = x^2
or y - sin(xy) = x²
Differentiating implicitly:

y' - cos(xy)*(xy' + y) = 2x

y' - xy'*cos(xy) - y*cos(xy) = 2x

y' = (2x + y*cos(xy))/(1 - x*cos(xy))

B.) y = arctan(x - 4)

dy/dx = 1/[(x - 4)² + 1]