Studying about the concept and seeing it on paper in the form of letters and numbers is one thing, but seeing how it occurs in our everyday lives is really eye-opening. I also appreciate the inclusion of the real life applications of the chain rule. The format of the explanation, as well as the easily digestible demonstrations of how to use the chain rule were really helpful in studying for the midterm exam as well, as there is a section dedicated to this very concept. I now more clearly understand how the rate of change, or slope, of one graph is connected to the rate of change of another and how to derive the derivative from those two slopes, as the variable y and x are related, and y is related to the variable z, thus connecting all variables in a composite of functions. I had previously still been a bit confused regarding how to utilize the chain rule to evaluate and find the derivative of a set of related graphs. I found this blog post to be exceptionally straightforward, easy to understand and, most importantly, helpful in communicating how to apply the chain rule in a number of various situations. Written by ats7016 Posted in Student posts 3 comments The horse expends energy at a rate 500 calories per 1 hour of walking.This relationship can also be represented in fractional form.If y = f(x) and z = g(y), then z depends on y, and y depends on x.Below are different ways to express this composition of functions. Composition of FunctionsĪ composition of functions is when one variable depends on another variable, which itself depends on another variable. The operations of addition, subtraction, multiplication (including by a constant) and division led to the Sum and Difference rules, the Constant Multiple Rule, the Power Rule, the Product Rule and the Quotient Rule. From this composition of functions, we can discern the functions’ derivatives and their relationships. Alternate Chain Rule Notation We have covered almost all of the derivative rules that deal with combinations of two (or more) functions. The Chain Rule is a mathematical method to differentiate a composition of functions.
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