CHAIN RULE
Remarks on use of the chain rule.
In general, when three variables x, y and z are connected by a chain of functional relations
then z depends on x. The dependence can be symbolized by
Suppose the original functions y(x) and z(y) are differentiable. Then the chain rule says that z(x) is also differentiable, and
In the application here, for mathematical purposes we regard v as depending on t through the chain of functions
then we have
What is doable is not always useful. Here it is productive to introduce y as the new independent variable because t, the original independent variable, does not appear in equation (1.2) except in the derivative, dv/dt.Copyright © 1998 Rensselaer Polytechnic Institute. All Rights Reserved.