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The first derivative of the function [co...

The first derivative of the function `[cos^(-1)(sin sqrt((1+x)/2))+x^x]` with respect to `x` at `x = 1` is

A

`3//4`

B

0

C

`1//2`

D

`-1//2`

Text Solution

Verified by Experts

`f(x)=cos^(-1)[cos""((pi)/(2)-sqrt((1+x)/(2)))]+x^(x)=(pi)/(2)-sqrt((1+x)/(2))+x^(x)`
`therefore" "f'(x)=-(1)/(sqrt(2))xx(1)/(2sqrt(1+x))+x^(x)(1+log x)`
`"or "f'(1)=-(1)/(4)+1=(3)/(4)`
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