#### Let's do basic

`Derivative`(衍生物或派生物) is some extracted thing from another thing. It may be a feature or characteristic, it's an abstract model for describing one thing in a higher view.

`Delta`(
) is a duration expressing the difference between two dates, time or date-time. We can seemly see this as a distance between two values.

`Differential` is a descriptor for describing the difference between two things.

Sometimes we can see `Delta` and `Differential` as the same thing.

#### Derivative notation

1. Original notation

2. Lagrange's notation

3. Leibniz's notation
   means small change. You can read it: `differential in x` over `differential in y` is `the derivative of that function`.

4. Newton's notation

#### What is derivative?

If it really has some meaning, that must be describing the average change in `y` when `x` get changed by this formula:

In that formula, when we assume that
(`the change in x`) is very small, near to 0, then
(`the change in y`) changes correspondingly. In that case, when the change in x and y is very small,
becomes a tending, indicated where y is about to going.

#### Graph derivative

Let me assume if we got a point A in a function curve.

The derivative of that function at that point is the slope of the tangent line at that point in that curve.

#### What function feature derivative described?

The
bigger on one point, the
of that function changes more when
increases. It seems the slop of the tangent line will steeper then.

The
smaller on one point until 0, the
of that function changes less when
decreases. It seems the slop of the tangent line gentler then.

If
is positive,
will going up.

If
is negative,
will going down.

It is the same thing if you replace
with
.

#### All in all

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