I've asked inductor questions before and never fully understood the answers.

First of all, I took calculus and learned derviatives as: X^3 d/dx = 3X^2.

The voltage across an inductor is given by: v= (L) di/dt

I'm unsure how to take the derivative of that formula because there is a di in the numerator.

I understand it can be said as delta i / delta t. But this would be in the case of t approaching 0 or a linear change in current; i.e. a linear ramp.

What if I had a poteniometer that was changing at an acceleration rate instead of a linear rate? Then my i would not be linear, it would be curved.

What if I wanted to know the current at exactly X seconds not using a delta assumption?

Any calculus assistance will be appreciated.

p.s. I am aware this formula can be used in Diff EQ and a formula will show the voltage at every point in time.