$\frac{\mathrm{dt}}{\mathrm{dx}}=2 \alpha \mathrm{x}+\beta$

$\frac{1}{\mathrm{v}}=2 \alpha \mathrm{x}+\beta$

$\text { (differentiating wrt time) }$

$-\frac{1}{\mathrm{v}^2} \frac{\mathrm{dv}}{\mathrm{dt}}=2 \alpha \frac{\mathrm{dx}}{\mathrm{dt}}$

$\frac{\mathrm{dv}}{\mathrm{dt}}=-2 \alpha \mathrm{v}^3$