if 2x^2+2x+ xy =2 and y(2)=-5 find y'(2) by implicit differentiation

Answer 1

Implicit differentiation:
(d/dx)(2x^2+2x+xy=2)
4x+2+y+xy'=0
y'(x)=-(4x+2+y(x))/x
y'(2)=-(4(2)+2+y(2))/2
=-(10-5)/2
=-5/2