if 2x^2+2x+ x = 2y and y(2)=-5 find y'(2) by implicit differentiation
2x^2 + 2x+x = 2y
(why 2x+x? If typo, fix and proceed)
4x + 2+1 = 2dy/dx
dy/dx = 2x + 3/2
At this point y(2) = -5 makes no sense.
If there's an unknown constant somewhere, fix things and the solve for c when y(2) = 5. Then figure y'(2)