If $f(x)=|\cos x-\sin x|$, then $f^{\prime}(\pi / 4)$ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

f(x)=|\cos x-\sin x|

, then

f^{\prime}(\pi / 4)

is equal to

View answer and explanation

Correct option: D

None of these

The correct answer is None of these because the left-hand derivative and right-hand derivative at x=π/4 are not equal, meaning the function is not differentiable at that point.

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

, then

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

is equal to Let

x

and

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and

x y=1

. The minimum value of

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is Let

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

where

[x]

denotes the integer part of

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. Then at

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being an integer, the left derivative of

f(x)

is If

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],

then

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

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

is equal to If

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

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

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