Solve the Problem $t$ Is Given By $s$ , Where $s^{3}+12 s t+4 t^{3}-5 t=0$

Multiple Choice

Solve the problem.
-The position of a particle at time $t$ is given by $s$ , where $s^{3}+12 s t+4 t^{3}-5 t=0$ . Find the velocity $\mathrm{ds} / \mathrm{dt}$ .

A) $\mathrm{ds} / \mathrm{dt}=\frac{5+12 \mathrm{~s}-12 \mathrm{t}^{2}}{3 \mathrm{~s}^{2}+12 \mathrm{t}}$
B) $d s / d t=\frac{5+12 s-12 t^{2}}{3 s^{2}-12 t}$
C) $\mathrm{ds} / \mathrm{dt}=\frac{5-12 \mathrm{~s}-12 \mathrm{t}^{2}}{3 \mathrm{~s}^{2}-12 \mathrm{t}}$
D) ds/dt $=\frac{5-12 s-12 t^{2}}{3 s^{2}+12 t}$