The value of $\frac{{dy}}{{dx}}$ at $x = \frac{\pi }{2}$, where $y$ is given by $y = {x^{\sin x}} + \sqrt x $, is

JEE MATHEMATICS MCQ: DIFFERENTIATION

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The value of

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

x = \frac{\pi }{2}

, where

y

is given by

y = {x^{\sin x}} + \sqrt x

, is

View answer and explanation

Correct option: A

1 + \frac{1}{{\sqrt {2\pi } }}

Option A (

1 + \frac{1}{{\sqrt {2\pi } }}

) is correct because it is the value of dy/dx at x=pi/2, calculated using logarithmic differentiation.

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}}