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?