How to find the derivative of F (x) = x ^ 2 * e ^ (- 2x), thank you,

How to find the derivative of F (x) = x ^ 2 * e ^ (- 2x), thank you,

F/(x)= 2xe^(-2x)-2x^2*e^(-2x)

If f (x) is in the domain of definition, its first derivative is greater than 0 and its second derivative is less than 0, then whether it increases monotonically or decreases monotonically, whether it is convex or concave

Monotonicity is the first derivative, the first derivative is greater than 0, increasing in the domain of definition
The second derivative is less than 0 and convex in the domain of definition

A high school mathematics problem (derivative) - there is a small problem like this: to prove that f (x) ≥ g (x) holds in the domain of definition
Can we use the following two inequalities to prove: 1. F (x0) ≥ g (x0) (x0 is the left end of the domain, and both functions are continuous) 2. F '(x) ≥ G' (x) (neither function has asymptote)
I asked the teacher, and the teacher said that my argument was not sufficient, so I didn't give an explanation,

The proof is correct;
I don't understand the reason why the teacher said it wasn't enough. Maybe he wanted to see such an auxiliary function proof
Let f (x) = f (x) - G (x)
F(x0)=0
F'(x)≥0
F(x)≥F(x0)=0
f(x)≥g(x)
[the above proof requires the domain to be an interval, such as [x0, b] or [x0, + ∞],
Not the union of several intervals]

Let y = f (x) = INX, y (n) y (n) is the derivative of order n
Is it just a rule?

Let's find the law. We can only find it in one order

What is this? Lt's a sheet
The horses are black and white
There are five people in my family
Singing and drawing are my hobbies
Are there many new students in your school

What are these? They are sheet
what color are these horses?
how many people are there in your family?
what are your hobbies?
No,there are not many new students in my school.

How to change this is a sheet into a plural sentence

Note: the singular and plural are the same

This is a sheet

These are sheep .
Note:
The singular is the same as the plural

How to change this is an apple into a plural sentence

these are apples

This is an apple and that is a
This is an apple and that is a plural sentence_ Brothers in the play is a countable noun brother__ In formal English, the place is divided into singular and singular___ Nouns. Countable nouns are divided into____ Nouns and___ Nouns. Countable nouns are singular and countable__ Two forms: to express a person or thing__ Form
Just fill in the blanks.

This is an apple and that is a write a plural sentence. These are the apples and that are. In the above sentence, the subject of these or those is be, the verb is (are), the noun is (plural). This and that are (Apple). Brothers in the sentence is countable noun brother

This is a young tree

There are young trees.