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


`(ds)/(dt) = (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.