Don't forget the chain rule with these.
#1:
#2:
The last one.
The best way to do these is the way earboth showed.
Take the partials with respect to x and y:
Same as above. See?.
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.