If x = t2, y = t3, then ("d"^2"y")/("dx"^2) is ______.

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If x = t2, y = t3, then ("d"^2"y")/("dx"^2) is 3/(4"t"). Explanation: Given that x = t2 and y = t3 Differentiating both the parametric functions w.r.t. t "dx"/"dt" = 2t and "dy"/"dt" = 3t2 $\therefore$ `"dy"/"dx" = ("dy"/"dt")/("dx"/"dt") = (3"t"^2)/(2"t") = $\frac{3}{2}$ "t" $\Rightarrow$ "dy"/"dx" = $\frac{3}{2}$ "t"` Now differentiating again w.r.t. x `"d"/"dx"("dy"/"dx") = $\frac{3}{2}$ * "dt"/"dx" $\Rightarrow$ ("d"^2"y")/("dx"^2) = $\frac{3}{2}$ * 1/(2"t") = 3/(4"t")`.

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