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
[tex]\dfrac{ds}{dt} = \dfrac{3t^2}{2s}[/tex]
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
[tex]2s \ ds = 3t^2 dt[/tex]
Integrating,
[tex]s^2 =t^3 + C[/tex]
We only need one constant of integration.
I won't bother to write the square root. This is choice D.
