If y = cos^{-1}(cos x),then find frac{dy}{dx} | vedclass

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(B) The function is given by $y = \cos^{-1}(\cos x)$.We know that $\cos^{-1}(\cos x) = x$ only when $x \in [0, \pi]$.Here,$x = \frac{5\pi}{4}$,which l

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$-1$

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(B) The function is given by $y = \cos^{-1}(\cos x)$.We know that $\cos^{-1}(\cos x) = x$ only when $x \in [0, \pi]$.Here,$x = \frac{5\pi}{4}$,which lies in the interval $(\pi, 2\pi)$.In the interval $(\pi, 2\pi)$,$\cos x = \cos(2\pi - x)$.Therefore,$y = \cos^{-1}(\cos(2\pi - x)) = 2\pi - x$.Differentiating with respect to $x$,we get $\frac{dy}{dx} = \frac{d}{dx}(2\pi - x) = -1$.Thus,at $x = \frac{5\pi}{4}$,$\frac{dy}{dx} = -1$.

If $y = \cos^{-1}(\cos x)$,then find $\frac{dy}{dx}$ at $x = \frac{5\pi}{4}$.

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