prove that the function f(x)=....has a derivative at x=0

prove that the function f(x)=....has a derivative at x=0

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\[f(x)=x²\cos \frac{ 1 }{ 2 }, when x \neq 0; 0, when x=0\]

Is that function typed correctly? I'm getting a very smooth looking parabola as my graph for that.

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