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If f(x) = ((a+x)/(b+x))^(a+b+2x) then pr...

If `f(x) = ((a+x)/(b+x))^(a+b+2x)` then prove that `f'(0) = [2log (a/b) + (b^2-a^2)/(ab) ](a/b)^(a+b)`

A

`((a)/(b))^(a+b)[2log((a)/(b))+(a^(2)-b^(2))/(ab)]`

B

`((a)/(b))^(a+b)[2log((a)/(b))-(a^(2)-b^(2))/(ab)]`

C

`((a)/(b))^(a+b)[2log((a)/(b))+(a^(2)-b^(2))/(2)]`

D

`((a)/(b))^(a+b)`

Text Solution

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The correct Answer is:
B
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