निम्नलिखित फलन का अवकलन गुणांक ज्ञात कीजिएः
`y=x+(x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+....oo`

Explanation

`y=x+(x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+....oo`
`therefore (dy)/(dx)=(d)/(dx)x+(1)/(2!)(d)/(dx)x^(2)+(1)/(3!)d/dxx^(3)+(1)/(4!)d/dxx^(4)+....oo`
`=1+(2x)/(2!)+(3x^(2))/(3!)+(4x^(3))/(4!)+.....oo`
`=1+(2x)/(2.1!)+(3x^(2))/(3.2!)+(4x^(3))/(4.3!)+.....oo`
`=1+x+(x^(2))/(2!)+(x^(3))/(3!)+....oo`
`=1+x+(x^(2))/(2!)+(x^(3))/(3!)+......oo`