derivative notation

[burnt mica]

just consolidating something

okay so if you have

dy/dx

do you read that as "the derivative of y with respect to x"

and is it in respect to x because it is in terms of x or for some other reason

like what do the two parts of the sentence mean
"the derivative of y with respect to x"

the two parts being

derivative of y and respect to x

I am only asking this because I am relatively far into learning derivatives and think I have a good intuitive understanding of them, but for some reason never consolidated this notation lol

<@&727457725017096242>

[stoic abyss]

yes

[inland sigil]

you could also say that it is in respect to x because dy/dx shows how quickly and in what direction y changes as x changes

so if it would be df/dt, you could say "how quickly and in what direction f changes as t changes"

and it is in terms of x (or t) because it shows the rate of change of y (or f) at that point with a fixed x (or t) value

for example, d(x^2)/dx = 2x, and after subbing, say, x = 5, we get 10, which means that rate of change of x^2 at x = 5 is equal to 10

[dry canyon]

y is the function, x is the variable you're measuring change in y with respect to. If y was a function of more than one variable, you could also take the derivative with respect to x, which would involve considering all other variables to be either constants or functions of x, depending on which they are. That's called a partial derivative.

[burnt mica]

thanks so much all of you!