Keep in mind that the derivative of a function is always one order of x lower than the function itself. To me, the function you posted resembles a cubic which is shifted left by 2 units and shifted up 5/2 units. Giving the function f(x) = (x-2)^3 + 5/2 and deriving that would give you something of the form 3(x-2)^2.

The derivative of a cubic is a quadratic and your graph should look something like the attachment.