If $x = {e^t}\sin t,y = {e^t}\cos t$, then $\frac{{{d^2}y}}{{d{x^2}}}$ at $x = \pi $, is

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Medium

1 of 1

Application +4 | -1

x = {e^t}\sin t,y = {e^t}\cos t

, then

\frac{{{d^2}y}}{{d{x^2}}}

x = \pi

, is

View answer and explanation

Correct option: D

\frac{2}{{{e^\pi }}}

Option D (

\frac{2}{{{e^\pi }}}

) is correct because after finding the first and second derivatives and substituting

t = \pi

, we get

\frac{{{d^2}y}}{{d{x^2}}} = \frac{2}{{{e^\pi }}}

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}}