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- anonymous

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

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- anonymous

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- anonymous

not the same thing

- anonymous

no thats different dy/dx is a derivatice
delta y and delta x are changes

- anonymous

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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- anonymous

the derivative can be written (in fact historically was almost always written) as
\[\lim_{\Delta x \rightarrow 0}\frac{\Delta y}{\Delta x}\]

- amistre64

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

- amistre64

the ghost of a departed value

- anonymous

but notice it is a limit that gives you
\[\frac{dy}{dx}\]as you take the limit, the greek letter becomes an english letter

- amistre64

god save the queen!!

- anonymous

sort of like
\[\sum\] and
\[\int\]

- anonymous

who you calling a queen?

- amistre64

♫♫...we are the champions .... ♫♫

- anonymous

oh of course.

- amistre64

what is the area of a circumference?

- anonymous

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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