Question

how do you find dy/dx by implicit differentiation

Answer 1

First you need an equation. Say you had x^2y+y^2=x. You take the derivative of both sides giving you 2xy+x^2dy/dx+2ydy/dx=1. Solve for dy/dx which you can treat as a variable. Note: the first expression was a chain rule hence no dy/dx in the first portion, and the dy/dx in the second portion of the derivative.