If $y = {\cos ^{ - 1}}\cos \left( {\left| x \right| - f\left( x \right)} \right)$, where $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1,if\,\,x > 0}\\ { - 1,if\,\,x < 0}\\ {0,if\,\,x = 0} \end{array}} \right.$ Then, $\left( {dy/dx} \right)x = \frac{{5\pi }}{4}$ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

y = {\cos ^{ - 1}}\cos \left( {\left| x \right| - f\left( x \right)} \right)

, where

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {1,if\,\,x > 0}\\ { - 1,if\,\,x < 0}\\ {0,if\,\,x = 0} \end{array}} \right.

Then,

\left( {dy/dx} \right)x = \frac{{5\pi }}{4}

is equal to

View answer and explanation

Correct option: B

Option B (1) is correct because, for x > 0, y = cos⁻¹(cos(x-1)), and for x in the interval [1, π+1], y = x-1, so dy/dx = 1.