If `y=1+x+x^2/(2!)+x^3/(3!)....x^n/(n!)`

Find by the definition the differential coefficient of the following: y=1+x/(1!)+x^2/(2!)+x^3/(3!)+……+x^n/(n!) show that dy/dx-y+x^n/(n!)=0

Statement 1: The coefficient of x^n in (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !))^3 is (3^n)/(n !) . Statement 2: The coefficient of x^n in e^(3x) is (3^n)/(n !)

Statement 1: The coefficient of x^n in (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !))^3 is (3^n)/(n !) . Statement 2: The coefficient of x^n in e^(3x) is (3^n)/(n !)

Statement 1: The coefficient of x^n is (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !))^3 is (3^n)/(n !) Statement 2: The coefficient of x^n ine^(3x)i s(3^n)/(n !)

If y = 1 + x + (x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+* * * +(x^(n))/(n!) prove that (dy)/(dx) + (x^(n))/(n!)=y*

Statement 1: The coefficient of x^(n) is (1+x+(x^(2))/(2!)+(x^(3))/(3!)+...+(x^(n))/(n!))^(3) is (3^(n))/(n!) Statement 2: The coefficient of x^(n)ine^(3x)is(3^(n))/(n!)

If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)-y+(x^n)/(n !)=0.

If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)-y+(x^n)/(n !)=0.

If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)-y+(x^n)/(n !)=0.

If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)-y+(x^n)/(n !)=0.