CPM Homework Help : APCALC Problem 6-8

You might think that $\frac{d}{dx}(2^x)=x\left(2^{x-1}\right)$ by the Power Rule. Unfortunately, this is not correct. Why not?

Hint:

The Power Rule applies to functions that have numeric exponents, such as

$y=x^{2},\ y=x^{3},\ y=x^{-1},\ y=x^{-2},\ y=x^{-\frac{1}{2}}\text{ and }y=x^{-\frac{1}{3}}.$

$y = 2^x$ does not fit the pattern. Explain why not.