Variation on Baby Rudin question - Differentiability

In Baby Rudin chapter 5 question 13, we have

$\displaystyle f(x) = \left\

x^asin({{\left | x \right |}^{-c}}) $ if x doesn't equal 0

$\displaystyle f(x) = 0$ if x=0.

I have got that f(x) is differentiable at 0 if a>1. Would this change if we make the absolute value of the initial x. That is, for what values of a is

$\displaystyle g(x) = \left\

|x|^asin({{\left | x \right |}^{-c}})$ if x doesn't equal 0

$\displaystyle g(x) = 0$ if x=0.

differentiable at 0?