# Derivative particle problem

the-rocketman
I have this function (to calculate potential for classical over-barrier model if you're wondering) where qp and qt are both (different) particle charges:

V(a,R) = -(qp /R) - [qt / (R-a)]

What is dV/da?

The maximum of the function occurs when dV/da = 0, and I need to solve for a. So does solving for a yield R[1 + sqrt(qt/qp)]^-1?

Thanks

Last edited:

the-rocketman said:
I have this function (to calculate potential for classical over-barrier model if you're wondering) where qp and qt are both (different) particle charges:

V(a,R) = -(qp /R) - [qt / (R-a)]

What is dV/da?

use the chain rule.

the-rocketman
Hm... but it has 2 variables. I haven't had any multivariable calc.

sic
what?
try to sketch the function. obviously, the function doesn't have a maximum for any constant R.
what is the question from the beginning?

the-rocketman
R and a are not constants, they are the variables. the constants are the q values

hypermorphism
the-rocketman said:
The maximum of the function occurs when dV/da = 0...
That isn't necessarily true for multivariable functions. Instead, you need to see when the gradient vector [dV/da, dV/dR] = 0 and use the discriminant to tell what type of critical point it is.

(the "d's" should be curly, like so: $$\partial$$)