## xEnOnn 4 years ago When we say $\frac{\mathrm{d} y}{\mathrm{d} x}$, it also be written as $\Delta x$ or $\Delta y$?

1. satellite73

not the same thing

2. jp32894

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

3. xEnOnn

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?

4. satellite73

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

5. 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

6. amistre64

the ghost of a departed value

7. satellite73

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

8. amistre64

god save the queen!!

9. satellite73

sort of like $\sum$ and $\int$

10. satellite73

who you calling a queen?

11. amistre64

♫♫...we are the champions .... ♫♫

12. satellite73

oh of course.

13. amistre64

what is the area of a circumference?

14. xEnOnn

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?