Hmmm...
Well, when you're using the Chain Rule, you take the exponent of the polynomial, multiply it by the whole expression and subtract the exponent by one, and you multiply all of that by the derivative of the original expression without the exponent.
So the first step would look like this:
4 (x^{2} + 2x + 7)^{3} d/dx (x^{2} + 2x + 7)
Now you can find the derivative of x^{2} + 2x + 7
Hope that helps