March 28, 2017

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What is wrong with the following reasoning???

f(x) = 2^x

f'(x) = x[2^(x-1)]

Although n x^(n-1) is the derivative of x^n, you cannot apply similar rules when x is the exponent and the number being raised to a power is a constant.

The derivative of b^x, where b is a constant, is ln(b) * b^x

For a proof, see http://math2.org/math/derivatives/more/b^x.htm

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