Inverse of a derivative

Physics Q&A
1

afbeelding

I was reading the lecture notes one last time before the exam and I came across the following part.

According to 2: dk/dE= (dE/dk)^-1 this isn’t always true right? I can think of a bunch of cases where it isn’t, or am I misinterpreting something?

Greetings,

Sjoerd

2

This identity is always true due to the inverse function rule. Note that it’s not just an inverse, but an inverse combined with a substitution.

3

Ah this explains a lot, thank you very much! I was just inverting in the 1 over x sense.