If $y = \cos^{- 1}{cos(|x| - f(x))}$, where $f(x) = \left\{ \begin{array}{r} 1,\ if\ x 0 \ - 1,\ if\ x

Question

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

Dr. Abubacker · Accepted Answer

(b)
Given, $y = \cos^{- 1}{\cos{(x - 1),\ \ \ x > 0}}$
$\Rightarrow \ \ \ \ y = x - 1,\ \ 0 \leq x - 1 \leq \pi$
$	herefore\ \ y = x - 1,\ \ \ \ \ \ \ \ \ \ \ \ 1 \leq x \leq \pi + 1$
At $x = \frac{5\pi}{4} \in \lbrack 1,\ \pi + 1brack$
$\Rightarrow \ \frac{dy}{dx} = 1\ \ \  \Rightarrow \ \ \ \left( \frac{dy}{dx} ight)_{x = \frac{5\pi}{4}} = 1$

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

Explanation

Reviewed by Dr. Abubacker

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