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

MCQ

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

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

✓

Answer

Correct option: D.

$\frac{3\text{t}}{2}$

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

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