I'm watching some tutorials on machine learning and know just enough calculus to have an intuition on what a derivative is, but that's it. But this question is bugging me so much that now I'm pretty much unable to keep watching the tutorial without thinking about it.
∂x means change in
x and I picture it as the length of the horizontal side of an infinitesimally small triangle drawn over the line of the function at the point x, y (you know, the typical triangle they draw when they first teach you calculus).
So I get why
∂y/∂x is written as a fraction and I seem to recall some cases in which operations are performed in it as if it were a fraction, which I'm fine with.
What really confuses me is that now I see this fraction written in the tutorial:
So he moved the
x part of the derivative outside the fraction and even added a multiplying symbol (which is what I understand by the blue dot) as if
∂ was multiplying the expression on the right.
So my question is, can
∂y be considered multiplications in any situation just like
∂y/∂x can be a fraction in some situations? Or is this just plain convention?