The Freshman's Product Rule (f⋅g)' = f'⋅g' is true only if f/f' + g/g' = 1pic.twitter.com/6eHFtV7BwI
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No Freshmen were harmed in the making of this tweet.
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We can construct a function satisfying the freshman's product rule from f(x), by solving the differential equation for g(x).
Try it out yourself! 
pic.twitter.com/GcWrV04O5g
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Did this back in high school when I worked at Subway. Also a good one is (f/g)' = f'/g' ...similar of course
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I just tried but something is missing.
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I am going to start over.
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I don't have the integral sign on my phone but here it is.pic.twitter.com/iDrpXmIdmU
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