Graphs of a function and its derivative

This demostration graphs (in black) a polynomial


            y = f(x) = A*x^4 + B*x^3 + C*x^2 + D*x + E  


and (in red) the derivative 

 
            f'(x) = A *(4*x^3) + B*(3*x^2) + C*(2*x) + D 


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Note:  The starting example has A=0, so the polynomial is a cubic (degree 3).