how many times can we differentiate this splitted function on point x=0

??

$\displaystyle

f(x) = \{ x^{2n} \sin (\frac{1}{x})

,x \ne 0

$

{0,x=0}

i did one differentiation

what to do next??

$\displaystyle

f(x)\; = \;x^2 \sin ({1 \over x}),x \ne 0

$

$\displaystyle

f'(0) = \mathop {\lim }\limits_{x \to 0} {{x^2 \sin ({1 \over x}) - 0} \over {x - 0}} = 0

$