'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 \[99!\]