I've been having some trouble grasping the conditions necessary to apply the chain rule to achieve the derivative of an algebraic expression or even apply it to a real world situation. So, my question to those skilled in qualitatively explaining the conditions for applying the Chain Rule and also when the Product Rule or Quotient Rule should be applied when the Chain Rule won't work. Essentially, I believe the Chain Rule is applied when it is possible to seperate a function into two seperate algebraic equations. Is this some sort of shortcut to not using the Product Rule or Quotient Rule in order to obtain the derivative of an equation? Is there more to that definition than I suspect? Are there situations where the Chain Rule cannot be used to obtain the derivative of a function? Thanks in advance.