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

Question

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

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Answer

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

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