'Chain' Rule Of Factorials

Calculus Level 1

If $y = 1 + x +\dfrac{x^2}{2!} +\dfrac{x^3}{3!} + \dfrac{x^4}{4!} + ...$ , find $\dfrac {dy}{dx}$ .

1!+2!+3!+\cdots+99!

Infinitely long functions are not differentiable

\infty

2!

1!

Same as the original function

99!