What is a partial derivative and how is it used in Schrodinger's equation?

[Arjun Wasan]

I am a 7th grader who is interested in Quantum mechanics and I'm learning schroninger's equation and there is a partial derivative in it and I looked it up but the best I could find was that it was a function of variables of the variables derivatives, but that didn't make much sense. Can someone please explain to me what a partial derivative is (I know what a derivative is already).

 

[fresh_42]

A partial derivative is a derivative with respect to only one coordinate while all others are treated as constants.
E.g. for $f(x,y,z) = 2x^2 +3yz + xz^2$ we get $\frac{\partial f}{\partial x} = 4x +z^2$.

Edit: And good luck! You can also look up basic terms on Wikipedia. It is something in between the short answer I gave you and the very long version of what could be said. Perhaps it's worth mentioning, that partial derivatives measure the slope along a coordinate direction, $x$ in the example above. You can always play a little with those functions on Wolfram. If you only use $x$ and $y$ as variables of a function they have nice plots.