Variation on Baby Rudin question

In Baby Rudin chapter 5 question 13, we have

$f(x) = \left\<br /> x^asin({{\left | x \right |}^{-c}})$ if x doesn't equal 0

$f(x) = 0$ 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

$g(x) = \left\<br /> |x|^asin({{\left | x \right |}^{-c}})$ if x doesn't equal 0

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

differentiable at 0?

Variation on Baby Rudin question - Differentiability