If `x=t^2` and `y=t^3` , find `(d^2y)/(dx^2)` .

Explanation

`x=t^{2} Rightarrow frac{d x}{d t}=2 t`
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y=t^{3} Rightarrow frac{d y}{d t}=3 t^{2}`
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Rightarrow frac{d y}{d x}=frac{3 t^{2}}{2 t}=frac{3}{2} t`
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therefore frac{d^{2} y}{d x^{2}}=frac{3}{2} times frac{d t}{d x}=frac{3}{2} times frac{1}{2 t}=frac{3}{4 t}`