I pledge my honor that I have abided by the Stevens Honor System 1 A composite function is 2 functions in which one is nested into another You use one function and apply its output to another function Yes the order does matter in which you compose 2 given functions because the 2 individual functions have different behaviors which changes the order in which you take the derivative of a composite function No because if one function h x outputs only complex numbers and has its respected composite function a x that accepts real numbers the function wouldn t make sense because the values won t match 2 The chain rule is when you take 2 individual functions in which they have 2 independent variables Calculating each function and then adding the slopes together won t make sense as you need to multiply each slope together to get the overall rate of change The chain rule was most likely derived from the other derivative rules such as the product and quotient Consequently the name chain rule is connected to the idea of a composite function 3 One real life example of the chain rule is how electric cars operate in which they take into many variables to determine the maximum fuel efficiency As the speed function is the first which also depends on the electric motor assisting the engine 4 Leibniz notation provides a clear representation model to express the chain rule As it substitutes functions with variables to make the composite function more concise A N A B N A C Spent 1 hour on this assignment