If 4x^2+3x+xy=1 and y(1)= -6, find y'(1) by implicit differentiation
4x^2+3x+xy=1
Implicit differentiation produces
8x + 3 + y + xy' = 0
xy' = - [ 8x + 3 + y]
y' = - [ 8x + 3 + y ] / x
And at the point ( 1, -6) we have
y ' = - [ 8(1) + 3 - 6] / 1 = - [ 5] / 1 = -5
