Differentiate the following with respect to x | vedclass

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Question

(A) Let $f(x) = \cos ^{-1}(\sin x)$.We know that $\sin x = \cos \left(\frac{\pi}{2} - x\right)$.Substituting this into the function,we get:$f(x) = \co

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(A) Let $f(x) = \cos ^{-1}(\sin x)$.We know that $\sin x = \cos \left(\frac{\pi}{2} - xight)$.Substituting this into the function,we get:$f(x) = \cos ^{-1}\left[\cos \left(\frac{\pi}{2} - xight)ight]$.Using the property $\cos ^{-1}(\cos 	heta) = 	heta$,we have:$f(x) = \frac{\pi}{2} - x$.Now,differentiating $f(x)$ with respect to $x$:$f'(x) = \frac{d}{dx}\left(\frac{\pi}{2} - xight) = 0 - 1 = -1$.Thus,the derivative is $-1$.

Differentiate the following with respect to $x$: $\cos ^{-1}(\sin x)$

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