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If y=e^x.e^(x^2).e^(x^3).......e^(x^n).....

If `y=e^x.e^(x^2).e^(x^3).......e^(x^n)....` for `0

A

e

B

4e

C

2e

D

3e

Text Solution

Verified by Experts

The correct Answer is:
B
Given , ` y = e^(x) . e^(x^(2)). e^(x^(3)) …e^(x^(n)) … "for" 0 lt x lt 1 `
`y= e^(x + x^(2) + x^(3)+...oo)`
`rArr y = e^((x)/(1-x) )rArr(dy)/(dx) = e^((x)/(1-x))[((1-x).1-x(-1))/((1 -x^(2)))]= e^((x)/(1-x)) = (1)/((1-x)^(2))`
`At x = (1)/(2) , (dy)/(dx) = e^(((1)/(2))/(1-1//2))xx(1)/((1-(1)/(2))^(2))=e xx2^(2) = 4e ` .
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF COMPOSITE FUNCTION (BY CHAIN RULE )
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