यदि `y=1+x+(x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(3!)+...,` तब `(dy)/(dx)` का मान ज्ञात कीजिएः।

Answer

`1+x+(x^(2))/(2!)+(x^(3))/(3!)+.....oo`

Explanation

`(dy)/(dx)=(d)/(dx)(1+x+(x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+.....) `
`=(d)/(dx)(1)+(d)/(dx)(x)+(1)/(2!)(d)/(dx)(x^(2))+(1)/(3!)(d)/(dx)(x^(3))+(1)/(4!)(d)/(dx)(x^(4))+....`
`=1+x+(x^(2))/(2!)+(x^(3))/(3!)+.....oo`