[SOUND] So let us proceed with
some basic definitions further. Firstly, let us can assume
the following annotations first. We start with the change of a function, which is simply how much
the value of function change from point a to some point x,
which is drawn on slide here. And also the same thing
applies to the argument, here is the change of the argument. We will call it delta f and
delta x, respectively. The thing that we
are actually interested in is the linear part of this function change. It's normally called a differential or DF. Basically the differential is
your childhood hopes and dreams. Because imagine that you were in
your childhood at the point a. And here we are assuming
that you are a super linear, it's the simplest function of all. And then you are supposed that you were
growing like a linear function and life was the most happiest life of all. And you've actually changed as a linear
function by your differential. Well, real life is not the simplest one. So this differential is not necessarily
coincides with the real function's change. So in order to understand
how they're connected, we need to introduce ourselves to
the concept of differentiable function. Differentiable function is basically
the things that we are expect from any decent function here,
where it's linear approximation, linear understanding of change,
is there a differential? It's kind of the same as function change. So we're actually mathematicians and works approximately without
any other continuation is kind of bad thing and
not exactly math here. So we need to define what is
approximately actually means. In our case it means that we infinitesimal
to the change of argument here. In our annotation, It is written as or
all from as functions argument. Well, the single variable functions,
as you may remember, is the simplest case. Errors here so
here being differentiable simply means that we are just
having a derivative. In other words, differentiable functions
are functions that can be closely fitted by straight lines or piece by straight
lines, which is kind of works, too. Now we are going to move to our Magics and try to calculate some basic
derivatives by definition. See you in the next
more interesting video.