1. sin(x+y) = x-y The answer is (1-cos(x+y))/((cos x+y)+1)

derivitive: cos(x+y)(1+dy/dx)=1-dy/dx

(dy/dx)+cos(x+y)(1+dy/dx)=1

(dy/dx)+cos(x+y)+cos(x+y(dy/dx))=1

(dy/dx)+cos(x+y(dy/dx))=1-cos(x+y)

I believe this is when i went wrong or something.

2. cos(xy)=1-x^2 the answer is (2x-y sin (xy))/(x sin (xy))

derivitive: -sin(xy)(x(dy/dx)+y)=-2x

2x-sin(xy)(x(dy/dx)+y)=0

And I got lost from here.

3.ln(xy)=e^2x The answer is (2e^2x-x^-1)y

derivitive: (1/xy)(xy'+y)=2e^2x

(-xy'+x-xy'+y)/(xy)^2=2e^2x

And then this step was when I got lost as to how this translates to the answer.