JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

f(x)=\frac{[x]}{|x|}, x \neq 0

, where [.] denotes the greatest integer function, then

f^{\prime}(1)

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Correct option: C

non-existent

Option C (non-existent) is correct because the left-hand derivative and right-hand derivative at x=1 are not equal, so the derivative does not exist.

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

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

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x y=1

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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}}

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