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

MCQ

If $x = t^2, y = t^3,$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2} =$

A
$\frac{3}{2}$
✓
$\frac{3}{4\text{t}}$
C
$\frac{3}{2\text{t}}$
D
$\frac{3\text{t}}{2}$

✓

Answer

Correct option: B.

$\frac{3}{4\text{t}}$

$\text{x}=\text{t}^2$
$\Rightarrow\frac{\text{dx}}{\text{dt}} = 2\text{t}$
$\text{y}=\text{t}^3$
$\Rightarrow\frac{\text{dy}}{\text{dt}} = 3\text{t}^2$
$\Rightarrow\frac{\text{dy}}{\text{dx}} = \frac{3\text{t}^2}{2\text{t}} = \frac{3\text{t}}{2}$
Hence, $\frac{\text{d}^2\text{y}}{\text{dx}^2} = \frac{3}{4\text{t}}$

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