How to Explain the Chain Rule: A Visual, Verbal, and Mathematical Approach

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Homework Statement



The question is: How would you explain the chain rule to a classmate?

My teacher wants: 1.a graph, 2. in words, 3. using math

Homework Equations




The Attempt at a Solution



I said: for the function y=f[g(x)], the chain rule is d/dx[g(x)].

Whats the graph like?
 
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What do you mean by d/dx[g(x)]?
 
DERIvative of g(x)...
 
You should have written it as: y'(x) = f'(g(x))g'(x). What you have written is not the chain rule.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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