Is there is a something like function of functions? I've seen an answer in which the user defined a function called $D$ where this function takes and input $f$ and gives output  $f'$
like an example : if $f(x)=x^2$ then $D(f)=f'=2x$
but is there is a something really like function of functions well acorrding to the function $D$ it takes a function as an input an gives another function as an output
but the definition of function that i've studied is that a function defined by it's graph where a function $f=$$\{ (a,f(a)) \}$ which is a set of ordered pairs
acorrding to this defintion then there isn't something called function of functions because we can't define a specific graph to it
like if we defined another function like $I$ where it takes input a function and gives it's integral out like \begin{gather} I(2x) =x^2 \end{gather}
we can't define a graph to this function
correct me if I said something wrong
 A: To answer your question up front: yes! Functions of functions are a thing, and a very important thing in many advanced fields of math.
In general, a "function" is any rule for turning inputs into outputs. If your input is itself a function, say $f(x) = x^2$, you can define a rule for generating a different, output function from this one, say by taking the derivative, $f'(x) = 2x$. Then the function $D$ which is defined by this rule, $D(f) = f'$, is in fact a function.
From a young age we are commonly trained to equate the word "function" with "function on the real numbers", or even more restrictively "function on the real numbers which can be expressed by one or many finite algebraic expressions, involving operations like $+$, $\cdot$, $\div$, exponentiation, integers and other named real constants like $e$ or $\pi$, and various special functions like trigonometric functions and logarithms" (by the way, such expressions define what are commonly called "elementary functions").
For this reason, when it comes to functions of functions, we often employ different terminology - we call them "operators" or "transformations" or something else to distinguish and emphasize the fact that we are thinking of these objects as things which transform or modify functions. But mathematically, they all fall under the definition of "function".
Also, as already mentioned in the comments, you can still use the idea of a graph to define a function of functions, but it is no longer something which you can draw or represent graphically. The input space is a collection of functions, and so is the output space, and we don't have a universally recognized geometric interpretation of "the space of all functions", nor do I think such an interpretation (that is useful) is even possible to come up with.
The formal definition of "function" is as a special case of a relation, which is roughly any rule for relating elements of one set to elements of another. For example, the relation "$xy$ is an even integer" describes a relation on the set of integers. Then $x = 2$ and $y = 3$ would relate under this rule, and so would $x = 2$ and $y = 4$ (as well as $x = 2$ and $y = $ any other integer at all, in fact).
A function is a special type of relation for which, for each choice of $x$, there is only a single $y$ such that $x$ relates to $y$. In other words, for each input there is only one possible output. This aligns with our usual concept of function because, for instance, if you pick a number and square it ($f(x) = x^2$), then there is only one possible answer to "what is the square of $x$?" Graphically, this property can be checked using something called the "vertical line test", which you may be familiar with from basic algebra.
A: 
"which is a set of ordered pairs"

Pairs of what? And the answer is that there is no restriction. They could be pairs of colors, of animals, or of functions. Now, admittedly, ordered pairs of real numbers is the only case where we can easily imagine the graph, and draw a nice picture of it, but we've taken the word "graph" and generalized it to also possibly refer to a collection of ordered pairs of kittens.
So yes, there are functions that take in functions and spit out functions, although, as noted in the comments, we often call them operators, just to help keep straight what's taking things in and what's being taken in.
By the way, you've only asked about higher order functions that take in and put out the same "kind" of mathematical object. But there's no restriction like this either. There are functions that take in functions, and return numbers. Two nice examples (where I'll leave out some details/restrictions for the sake of simplicity) are
$$ \textrm{Definite integral:     } T(f) = \int_0^2 f(x) dx$$
$$\textrm{Point evaluation:     } E_3(f) = f(3)$$
(Of course the interval of integration ($[0,2]$), or the point you evaluate at ($x=3$), can be changed, so these are in fact entire families of functions defined on functions.)
And just like it's traditional to call the functions that map functions to functions "operators", functions that map functions to numbers are often called "functionals". But again that's just a bit of terminology to help us keep things straight, not a profound difference - they're all just functions.
