What is implicit differentiation?

• An equation connecting?x?and?y?is not always easy to write?explicitly?in the form?y=?f(x)?or?x?=?f(y)
• However you can still differentiate such an equation?implicitly?using the?chain rule:

• Combining this with the?product rule?gives us:

• These two special cases are especially useful:

• When?x?and?y?are connected in an?equation?you can differentiate both sides with respect to?x?and rearrange to find a formula (usually in terms of?x?and?y?) for?dy/dx
  • Note that?dy/dx?is a single algebraic object
  • When rearranging do not treat?dy/dx?as a fraction
  • Especially do not try to separate?dy?and?dx?and treat them as algebraic objects on their own!