If `x=t^2,\ \ y=t^3` , then `(d^2y)/(dx^2)=` `(a)3//2` (b) `3//4t` (c) `3//2t` (d) `3t//2`

Explanation

Correct option is B)


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