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By now, you've probably covered basic differentiation of a function y in terms of a single variable x. This is called explicit differentiation.

Implicit differentiation, on the other hand, is differentiating a variable in terms of another variable. We're not just taking the derivative of x or 8x+6 anymore, we're taking the derivative of whole equations like y = 8x+6 to find dy/dx.

〰️ Explicit:

  • Single variable function/relation
  • Example:

〰️ Implicit:

  • More than one variable in the function/relation
  • Example: 


So how do you do implicit differentiation? Just apply the chain rule!

🌟 Example:

We can even simplify further to solve for dy/dx!


...And there you have it!

Implicit differentiation is useful in solving differential equations, where you'll need to solve for dy/dx. Some applications include optimization, e.g. finding the rate of change of volume with respect to the rate of change of time.

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