Which one of the following is true when ds/st =3t^2/2s

Middle school math!  I actually know how to teach differential calculus to middle schoolers, but I wouldn't start with this example, where we're gonna have to integrate eventually.

We have



We have an odd mix of s and t on the right, which means this probably was an implicit derivative to begin with.  In other words, instead of s as a function of t, we have some equation of s and t that is satisfied.

We move the variables to their respective sides 



Integrating,



We only need one constant of integration.

I won't bother to write the square root. This is choice D.