Original
You might be wondering, given a plot {{MATH_398}},
{{CMD_399}}
What's the difference between {{MATH_400}} and {{MATH_401}}? What about
{{MATH_402}} and {{MATH_403}}?
{{CMD_404}}
Regardless, it is now a pressing question. Here's the deal:
{{MATH_405}}
is the {{CMD_406}} of {{MATH_407}} with respect to {{MATH_408}}.
On the other hand:
{{MATH_409}}
is the {{CMD_410}} of {{MATH_411}} with respect to
{{MATH_412}}. Essentially, {{MATH_413}} and {{MATH_414}} are the same type of thing,
they are (usually small) changes in {{MATH_415}}. However, {{MATH_416}} and {{MATH_417}} are very different things.
{{CMD_418}}
{{CMD_419}} {{MATH_420}}; it is the change in {{MATH_421}} associated to {{MATH_422}}.
{{CMD_423}} {{MATH_424}}, it is the change in {{MATH_425}} associated to {{MATH_426}}.
{{MATH_427}}
Note: {{MATH_428}}.
So, the change
{{ENV_429}}
{{CMD_430}}
{{CMD_431}}
Suppose {{MATH_432}}. If we are at the point {{MATH_433}} and {{MATH_434}}, what is {{MATH_435}}? What is {{MATH_436}}?
{{CMD_437}}
{{MATH_438}}
{{CMD_439}}
{{CMD_440}}
{{MATH_441}}
{{CMD_442}}
{{CMD_443}}
{{MATH_444}}
{{CMD_445}}
{{CMD_446}}
Differentials can be confusing at first. However, when you master
them, you will have a powerful tool at your disposal.