if y=1+x+x^2/2!+x^3/3!+ +x^n/n! show that dy/dx+x^n+n!=y - Maths - Limits and Derivatives

Question

if y=1+x+x^2/2!+x^3/3!+ +x^n/n! show that
dy/dx+x^n+n!=y

Neha Sethi · Accepted Answer

Dear student
We have,y=1+x1!+x22!+x33!+x44!+
+xn-1n-1!+xnn!∴dydx=0+11!+2x2!+3x23!+4x34!+
+n-1xn-2(n-1)!+nxn-1n!⇒dydx=1+x1!+x22!+x33!+
+xn-1(n-1)!⇒dydx=1+x1!+x22!+x33!+
+xn-1(n-1)!+xnn!-xnn!⇒dydx=y-xnn!⇒dydx+xnn!=y
Regards

if y=1+x+x^2/2!+x^3/3!+.+x^n/n! show that dy/dx+x^n+n!=y

if y=1+x+x^2/2!+x^3/3!+.+x^n/n! show that
dy/dx+x^n+n!=y