[BUG] multivariable chain rule

[Tevian Dray]

Can anyone provide a good example of the use of the multivariable chain rule?
Seems to me that most purported examples don't actually involve the chain rule
at all.  For instance, if V=IR and 1/R=1/R1+1/R2, the computation of dV/dt
doesn't really use the chain rule (with V=V(I,R) and everything else a
function of t), but rather the product and power rules.  In fact, I claim the
only time one actually needs the multivariable chain rule is when one does NOT
explicitly know the functional dependence.  In the above example, that means
not knowing how V depends on I and R.  This is very relevant for theoretical
discussions, such as changing variables in a PDE.  But what purpose does it
serve in a multivariable calculus course?

Tevian