If $f(x) = |\cos x|,$ then ${f^\prime }\left( {\frac{\pi }{4}} \right)$ is equal to ……..

If $f(x) = |\cos x|,$ then ${f^\prime }\left( {\frac{\pi }{4}} \right)$
$0 < x < \frac{\pi }{2},\cos x > 0$
$f(x) = + \cos x$

therefore,${f^\prime }(x) = ( - \sin x)$

$\Rightarrow$ ${f^\prime }\left( {\frac{\pi }{4}} \right) = - \sin \frac{\pi }{4} = \frac{{ - 1}}{{\sqrt 2 }}$