If x = t^2 , y = t^3 , then d^2 y d x^2 = - Vidyadip

MCQ

If $x = {t^2}$, $y = {t^3}$, then ${{{d^2}y} \over {d{x^2}}} =$

A
${3 \over 2}$
✓
${3 \over {(4t)}}$
C
${3 \over {2(t)}}$
D
${{3t} \over 2}$

✓

Answer

Correct option: B.

${3 \over {(4t)}}$

b
(b) $\frac{{dy}}{{dx}} = \frac{{dy/dt}}{{dx/dt}} = \frac{{3{t^2}}}{{2t}} = \frac{3}{2}t = \frac{3}{2}\sqrt x $

$\Rightarrow \frac{{{d^2}y}}{{d{x^2}}} = \frac{3}{{4\sqrt x }} = \frac{3}{{4t}}$.

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