Imagine the conversation that came before this response? Response: For example, it might happen that "f" is constrained to a curve formula_85.
Conversation transcript:
 Person A) What does it mean in terms of total derivatives?.
 Person B) It says that, for two functions formula_1 and formula_78, the total derivative of the composite formula_79 at formula_11 satisfies If the total derivatives of formula_1 and formula_78 are identified with their Jacobian matrices, then the composite on the right-hand side is simply matrix multiplication..
 Person A) Are there any other interesting aspects about this article?.
 Person B) This is enormously useful in applications, as it makes it possible to account for essentially arbitrary dependencies among the arguments of a composite function..
 Person A) What kind of applications are there?.
 Person B) Suppose that "f" is a function of two variables, "x" and "y"..
 Person A) What else can you tell me about the applications?.
 Person B) If these two variables are independent, so that the domain of "f" is formula_84, then the behavior of "f" may be understood in terms of its partial derivatives in the "x" and "y" directions..
 Person A) Is there anything else that is important?.
 Person B) However, in some situations, "x" and "y" may be dependent..
 Person A) What are some examples of the variables being dependent?.
 Person B) 