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The value of differentiation of e^(x^(2...

The value of differentiation of ` e^(x^(2))` with respect to `e^(2x-1)`
at x = 1 is

A

e

B

0

C

`e^(-1)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
Let ` u = x^(x^(2)) and v = e^(2x-1)`
On differentiating both functions w.r.t.x, we get
` (du)/(dx) = e^(x^(2)) . 2x and (dv)/(dx) = e^(2x-1).2 `
` therefore (du)/(dx) = (e^(x^(2)). 2x)/(e^(2x-1).2) rArr (du)/(dv) xe^(x^(2-2x +1))`
`rArr ((dv)/(dx))_((x=1))=1.e^(1-2+1)=1 `
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