Question

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

Answer 1

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

$\dfrac{ds}{dt} = \dfrac{3t^2}{2s}$

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 

$2s \ ds = 3t^2 dt$

Integrating,

$s^2 =t^3 + C$

We only need one constant of integration.

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