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When we say \[\frac{\mathrm{d} y}{\mathrm{d} x}\], it also be written as \[\Delta x\] or \[\Delta y\]?

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not the same thing
no thats different dy/dx is a derivatice delta y and delta x are changes
Isn't the derivative the change? Like for dy/dx, it is the change in the y-axis for each x value? When what are delta x and delta y?

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Other answers:

the derivative can be written (in fact historically was almost always written) as \[\lim_{\Delta x \rightarrow 0}\frac{\Delta y}{\Delta x}\]
put your hands 14 inches apart; \(\Delta\)x = 14 inches; as you bring your hands together that \(\Delta\)x gets smaller and smaller. The moment your hands touch and the distance is gone; you have reached dx
the ghost of a departed value
but notice it is a limit that gives you \[\frac{dy}{dx}\]as you take the limit, the greek letter becomes an english letter
god save the queen!!
sort of like \[\sum\] and \[\int\]
who you calling a queen?
♫♫...we are the champions .... ♫♫
oh of course.
what is the area of a circumference?
So the delta x is the change in the x value, while the dy/dx is the rate of change, the gradient. Since the gradient is the rate of change, I remember the gradient is a function that tells the increase in the y-axis for every increment of x value on the x-axis, is this right? Then this gradient tells a change in the y-axis for each increment of x value, is delta y or delta x?

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