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Calculating with value instead of symbol


I need to calculate the following sequence:

W=x^2
Y[x_]:=x W

If I differentiate Y[x] in respect to x, 
I get different solutions, depending on the employed function,

Y'[x]   or   D[Y[x], x], 

because Y is defined as Y[x]=x W and not as Y[x]= x^3. 
How can I get Mathematica to work with the value of W to receive the 
Y[x]= x^3?

Thank you very much for your help,

Andreas Groehn

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