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Differentiation question

2022 · 28 Jul · Shift 2 · Q28

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JEE Main
Mathematics
Differentiation
2022 · 28 Jul · Shift 2 · Q28

Differentiation question

2022 · 28 Jul · Shift 2 · Q28

JEE MainMathematicsDifferentiationMCQ+4 / −1

Let

x(t)=2 \sqrt{2} \cos t \sqrt{\sin 2 t}

and

y(t)=2 \sqrt{2} \sin t \sqrt{\sin 2 t}, t \in\left(0, \frac{\pi}{2}\right)

. Then

\frac{1+\left(\frac{d y}{d x}\right)^{2}}{\frac{d^{2} y}{d x^{2}}}

at

t=\frac{\pi}{4}

is equal to :

A
$\frac{-2 \sqrt{2}}{3}$
B
$\frac{2}{3}$
C
$\frac{1}{3}$
D
$\frac{-2}{3}$

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