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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(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 $x = \frac{5\pi}{4}$.

Similar Questions

If $\log_{\pi}x > 0$,then the value of $\log_{\pi}\left( \sin^{-1}\frac{2x}{1+x^2} + 2\tan^{-1}x \right)$ is equal to

Simplify $\tan ^{-1}\left[\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right],$ if $\frac{a}{b} \tan x > -1$.

If $\pi \leq x \leq 2 \pi$,then $\cos^{-1}(\cos x)$ is equal to :-

$\sin^{-1}x + \sin^{-1}\frac{1}{x} + \cos^{-1}x + \cos^{-1}\frac{1}{x} = $

If $\tan^{-1} (x+ 2)+ \tan^{- 1}( x -2)= \tan^{-1} (\frac{1}{2}),$ then the sum of the value$(s)$ of $x$ is equal to-

Vedclass Test Series

Exam Paper Generator

Online Exam Module