If $y = {\cos ^{ - 1}}(\cos x),$ then $\frac{{dy}}{{dx}}$

${\rm{ - 1}}$ in the whole plane

1 in the 2nd and 3rd quadrants of the plane

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

y = {\cos ^{ - 1}}(\cos x),

then

\frac{{dy}}{{dx}}

View answer and explanation

Correct option: D

\mathrm{ - 1}

in the 3rd and 4th quadrants of the plane

The correct answer is D (

\mathrm{ - 1}

in the 3rd and 4th quadrants of the plane) because the derivative of

y = \cos^{-1}(\cos x)

is -1 for

\pi < x \le 2\pi

, which corresponds to the 3rd and 4th quadrants.

Practice All Chapter MCQs →

f(x)=|x|^{|\tan x|}

f^{\prime}\left(\frac{-\pi}{6}\right)

x

y

x>0

x y=1

x+y

f(x)=[x] \sin (\pi x)

[x]

x

x=k, k

f(x)

y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

z = y + f\left( v \right),

v = \left( {\frac{x}{y}} \right),

v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}