Mathematics Problem, #120

A colleague Bill Wardlaw (March 3, 1936-January 2, 2013) used to create a “Problem of the Week” for his students, giving a prize of a cookie if they could solve it. Here is one of them.

Mathematics Problem, #120

A calculus 1 student Joe asks another student Bob “Is the following expression correct?” and writes

f'(x^3)=3x^2
on the blackboard. Bob replies, “Well, it could be, but I don’t think that is what you mean.”

Find a function that makes what Joe said correct.

Solution to #119:
There are (16!)/(2^8) (about 82 billion) different orders that the spider can put on shoes and socks.

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