dy/dx= ?

Question

if
y=1+x+(x^2/2)+(x^3/6)+(x^4/24)+(x^5/120)+(x^6/720)+(x^7/5040).....

Answer 1

Observe that:
y = sum{n=0 to infty} x^n /n!

y = 1 + sum{n=1 to infty} x^n /n!

Take the derivative and simplify.
...

Then expand.

Hint: the expansion should look familiar.