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

MCQ

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

A
$-\frac{1}{\text{t}^2}$
B
$\frac{1}{2\text{at}^3}$
C
$-\frac{1}{\text{t}^3}$
✓
$-\frac{1}{2\text{at}^3}$

✓

Answer

Correct option: D.

$-\frac{1}{2\text{at}^3}$

$\text{x}=\text{at}^2,\text{y}=2\text{at}$
$\frac{\text{dy}}{\text{dx}}=\frac{\frac{\text{dy}}{\text{dt}}}{\frac{\text{dx}}{\text{dt}}}=\frac{2\text{a}}{2\text{at}}$
$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{dy}}{\text{dx}}\Big)=\frac{\frac{\text{d}}{\text{dt}}\Big(\frac{\text{dy}}{\text{dx}}\Big)}{\frac{\text{dx}}{\text{dt}}}$
$=\frac{\frac{-1}{\text{t}^2}}{2\text{at}}=\frac{-1}{2\text{at}^3}$

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