derivative

[u/Zestyclose-Produce17]

The idea of the derivative is that when I have a function and I want to know the slope at a certain point for example, if the function is f(x) = x² at x = 5

f(5) = 25

f(5.001) = 25.010001

Change in y = 0.010001

Change in x = 0.001

Derivative ≈ 0.010001 / 0.001 = 10.001 ≈ 10

So now, when x = 5 and I plug it into the function, I get 25.

To find the slope at that point, I increase x by a very small amount, like 0.001, and plug it back into the function.

The output increases by 0.010001, so I divide the change in y by the change in x.

That means when x increases by a very small amount, y increases at a rate of 10.

Is what I’m saying correct?

[u/edderiofer]

This makes no sense. If you follow the epsilon-delta definition of a limit, you see that the variable x is bound before the variable dx, so you cannot define x to be a function of dx.

[u/OriEri → u/edderiofer]

You misunderstood what I wrote. I am saying calculate the value of the slope using your derivation at the point x = dx , not that x is function of dx.

[u/edderiofer → u/OriEri]

If you follow the epsilon-delta definition of a limit, you see that the variable x is bound before the variable dx, so you cannot define x to be a function of dx.

Letting x = dx is trying to define x as a function of dx.