This question refers to lecture 6 of the Single Variable Calculus course, where Dr. Jerison is showing how to calculate d/dx a^x.
(18-01sc-single-variable-calculus-fall-2010
Session 17: The Exponential Function, its Derivative, and its Inverse)
Isn't there an error at 18:12 of the lecture?
The equation d/dx f(kx) = k f'(kx) mixes Newton's and Leibnitz's notation, but, using Newton's, the equation is f'(kx) = k f'(kx).
It seems this could only be correct for k=1 (or f'(kx) = 0).
But k is "any number", not just 1; and f'(kx) = 2^(kx) ln(kx), so f'(kx) could only be 0 if kx = 1.
Well, that rules out k being "any number - it has to be the reciprocal of x - and it couldn't be 0.
Any help explaining this apparent difficulty with the proof would be appreciated.
Thanks.

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