106. Implicit Differentiation

When a function is not explicitly solved for one variable in terms of another. E.g.:

Instead of solving for explicitly in terms of , implicit differentiation allows you to differentiate both sides of an equation directly, treating as an implicit function of .

Steps for Implicit Differentiation

  1. Differentiate both sides of the equation with respect to , treating y as a function of

  2. Apply the chain rule whenever differentiating , since

  3. Solve for

Example
  1. Differentiate both sides
  1. Apply the chain rule to
  1. Slove for