JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

f\left( x \right) = \left\{ {\frac{\pi }{2}\left[ x \right] - {x^5}} \right\},1 < x < 2

and [.] denotes the greatest integer function, then

f'\left( {\sqrt[5]{{\frac{\pi }{2}}}} \right)

is equal to

View answer and explanation

Correct option: C

- 5{\left( {\pi /2} \right)^{\frac{4}{5}}}

Option C (

- 5{\left( {\pi /2} \right)^{\frac{4}{5}}}

) is correct because after evaluating the derivative at the given point, the result is

- 5{\left( {\pi /2} \right)^{\frac{4}{5}}}

More Questions from DIFFERENTIATION

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

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

x

y

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x y=1

x+y

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[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}}