If variables $x$ and yare related by the equation $x = \mathop \smallint \nolimits_0^y \frac{1}{{\sqrt {1 + 9{u^2}} }}du,$ then $\frac{{{d^2}y}}{{d{x^2}}}$ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Medium

1 of 1

Application +4 | -1

If variables

x

and yare related by the equation

x = \int \nolimits_0^y \frac{1}{{\sqrt {1 + 9{u^2}} }}du,

then

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

is equal to

View answer and explanation

Correct option: C

9y

Option C (

9y

) is correct because after differentiating the given equation twice and simplifying, we find that

\frac{{{d^2}y}}{{d{x^2}}} = 9y

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}}