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If $y=\cos ^{-1}(\cos x)$, then find $\frac{d y}{d x}$ at $x=\frac{5 \pi}{4}$
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The correct answer is:
-1
$\begin{aligned} & y=\cos ^{-1}(\cos x) \\ & y=\cos ^{-1}(\cos (2 \pi-x)) \quad[\because x \in(\pi, 2 \pi)]\end{aligned}$
$\begin{aligned} y & =2 \pi-x \\ \frac{d y}{d x} & =-1\end{aligned}$
$\begin{aligned} y & =2 \pi-x \\ \frac{d y}{d x} & =-1\end{aligned}$
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