leads us to consider treating derivatives as fractions, so that given a composite function y(u(x)), we guess that
This speculation turns out to be correct, but we would like a better justification that what is perhaps a happenstance of notation. Let's start with the definition of the derivative and try to arrive at this result:
Given: y = f(u(x)).
By simple algebra, we know that
Differentiablility implies continuity; therefore
Then, we have
which is the Chain Rule.