IMPLICIT differentiation!!?

Question

if x+xy+y^2=7, find dy/dx at (1,2)....
Thanks so much!!!

Answer 1

The derivative would be
1 + x(dy/dx) + 1y + 2y(dy/dx) = 0
(You use the product rule on the middle term.)

Now you need to solve for dy/dx, so get the terms with (dy/dx) on one side and those without on the other.

x(dy/dx) + 2y(dy/dx) = -1 - y
(dy/dx)(x + 2y) = -1 - y
dy/dx = (-1 - y) / (x + 2y)

Now plug in (1,2).

(-1 - 2) / (1 + 2*2) = -3/5