If y = | x - | x|| , then the value of (dy)/(dx) at x = (5π)/(4) is

In the neighbourhood of $x = \dfrac{5\pi}{4}, sin x < 0$
$∴ \left|\sin x\right| = - sin x$
Now, $y = \left|\tan x - ( - sin x )\right| = \left|\tan x + sin x\right|$
Now, in the neighbourhood of $x = \dfrac{5\pi}{4}$
$tan x + sin x ≃ 1 + \left(- \dfrac{1}{2}\right), which is positive<br />$∴ y = tan x + sin x$<br />Hence, \dfrac{dy}{dx} = \sec^{2}$ x + cos x$<br />Putting$x = $\dfrac{5\pi}{4}, we get,</p><p>\dfrac{dy}{dx} = \left(- \sqrt{2}\right)2 - \dfrac{1}{2} = \dfrac{2\sqrt{2} - 1}{2}$