1.

Differentiate the following w.r.t. x:`e^x+e^x^2+. . . .+e^x^5`

Answer» `"Let"y = e^(x) + e^(x^(2)) + e^(x^(3)) + e^(x^(4)) + e^(x^(5))`
`rArr (dy)/(dx) = (d)/(dx) (e^(x) + e^(x^(2)) + e^(x^(3)) + e^(x^(4)) + e^(x^(5)))`
`=e^(x) + e^(x^(2)) (d)/(dx) x^(2) + e^(x^(3))(d)/(dx) x^(3) + e^(x^(4))(d)/(dx) x^(4) + e^(x^(5))(d)/(dx) x^(5)`
`=(e^(x) + 2x* e^(x^(2)) + 3x^(2)* e^(x^(3)) + 4x^(3)* e^(x^(4)) + 5x^(4)*e^(x^(5)))`


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