If 5x^2+3x+xy=2 andy=-12, find y'(2) by implicit differentiation.

Answer 1

I get
10x + 3 + x(dy/dx) + y = 0
dy/dx = -(10x + 3 +y)/x

so when y = -12 your original equation becomes
5x^2 - 9x - 2 = 0
(5x+1)(x-2) = 0
x = -1/5 or x = 2
so we want dy/dx when x=2 and y = -12

plug those values in and you got it.