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

If `y=1+ x/(1!)+x^2/(2!)+x^3/(3!)+......,` then `(dy)/(dx)`

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Given, `y=1+x/(1!)+x^(2)/(2!)+x^(3)/(3!)+x^(4)/(4!)+……….`
`therefore (dy)/(dx) = 0+1+(2x)/(2) + (3x^(2))/(6) + (4x^(3))/(4!)`
`=1+x+x^(2)/2+x^(3)/6+………………..`
`=1+x/(1!)+x^(2)/(2!) + x^(3)/(3!)+……..`
=y
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