Question

If x = t², y = t³, then $\frac{d^{2}y}{d{x}^2}=$

(a) 3/2
(b) 3/4t
(c) 3/2t
(d) 3t/2

Answer 1

(b) 3/4t

Here,
$$\begin{gathered} x=t^2\mathrm{and}y=t^3 \\ \Rightarrow \frac{\mathit{d}x}{\mathit{d}t}=2t\mathrm{and}\frac{\mathit{d}y}{\mathit{d}t}=3t^2 \\ \therefore \frac{\mathit{d}y}{\mathit{d}x}=\frac{3t}{2} \\ \Rightarrow \frac{{\mathit{d}}^{2}y}{\mathit{d}{x}^2}=\frac{3}{2}\frac{dt}{dx}=\frac{3}{4t} \end{gathered}$$