example: if f(x) = cosh(x), what is f'(x)?
this problem produces the answer (daughter) f(x) = sinh(x).
repeating the problem using the daughter function you get: if f(x) = sinh(x), what is f'(x)?
this daughter problem produces the answer (granddaughter) if f(x) = cosh(x), what is f'(x)?, which is the original problem (so grandma = granddaughter).
makes sense to me. I think this guy should spend more time trying to learn math rather than trying to prove his teacher knows nothing.
also, using sound waves are sine waves, so showing how, say 3sin(x) sounds different than sin(3x) is a good way to learn what they are. (in my example, the 3sin(x) would be much higher pitched and three times as loud as the sin(3x).
Not that it is important, but sin(3x) would have 3 times the frequency of sin(x) and an octave is just double the frequency. I do like the 3 times louder part of your explanation.