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Let us define

r1 = 1;r2 = 2;

and

beta2[t_] := {r1*Cos[2*Pi*t], r2*Sin[2*Pi*t]}
beta1[t_] := beta2[t + 4.8*t^2*(t - 1)^2] 
k[v_] := If[Norm[v] > 0, v/Sqrt[Norm[v]], 0]

with

q2[t_] :=  FunctionExpand[k[beta2'[t]], Assumptions -> t \[Element] Reals]

q1[t_] :=  FunctionExpand[k[beta1'[t]], Assumptions -> t \[Element] Reals]

Now when I call

 q1'[3]

I get

{4.56985 + 0.157049 (10.2293 Derivative[1][Abs][-5.97566] - 40.9174 Derivative[1][Abs][-3.88322]), -28.1291 + 0.102057 (10.2293 Derivative[1][Abs][-5.97566] - 40.9174 Derivative[1][Abs][-3.88322])}

Question

How to simplify this expression?

share|improve this question
    
Apply FunctionExpand to the final expression to simplify it. Sorry, I didn't follow the rest of the code ... –  Szabolcs Mar 29 at 20:34
1  
You can't take derivative with respect to a number. so not sure what q1'[3] is meant to represent. Also, If[Norm[v] > 0, v/Sqrt[Norm[v]], 0] return the result you show, since it is passed a symbolic expression. You are mixing symbolic with numerical computation in strange way. –  Nasser Mar 29 at 23:40

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