If we think of this intuitively, the degree of the expression is 99 because (x^7)^10*(x^2)^11*(x^7)=x^99. So is we were to multiply it all out (which is not feasible) we would have the leading term be x^99.
The first derivative of that term is 99x^98, the second is 99*98*x^97, the third is 99*98*97*x^96 which is we do the 99th derivative is have 99*98*97*96*...4*3*3*2*1* x^0=99!
99! is a constant and the derivative of that is 0.
So basically, all terms will cancel out by the 100th derivative.
