If `f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2)` is (a) `(sqrt(pi))/6` (b) `-sqrt(pi//6)` (c)`1//sqrt(6)` (d) `pi//sqrt(6)`

Options

A. `sqrt(pi//6)`
B. `-sqrt(pi//6)`
C. `1//sqrt(6)`
D. `pi//sqrt(6)`

Explanation

`f(x)=sqrt(1+cos^(2)(x^(2)))`
`therefore" "f'(x)=(1)/(2sqrt(1+cos^(2)(x)^(2)))(2 cos x^(2))(- sin x^(2))(2x)`
`(-x sin 2x^(2))/(sqrt(1+cos^(2)(x^(2))))`
`"or "f'((sqrt(pi))/(2))=(-(sqrt(pi))/(2)sin""(2pi)/(4))/(sqrt(1+cos^(2)""(pi)/(4)))=(-(sqrt(pi))/(2)1)/(sqrt((3)/(2)))`
`therefore" "f'((pi)/(2))=-sqrt((pi)/(6))`