On the derivative of function! F (x) = 2x ^ 3-6x ^ 2 + 7 f(x)=2x^3-6x^2+7 Why is it so difficult to derive f'(x)=6x^2-12x instead of f(x)=6x^2+7 What I want is why! It's not the next solution!

On the derivative of function! F (x) = 2x ^ 3-6x ^ 2 + 7 f(x)=2x^3-6x^2+7 Why is it so difficult to derive f'(x)=6x^2-12x instead of f(x)=6x^2+7 What I want is why! It's not the next solution!

7 is a constant, derivative = 0
The derivative of 6x ^ 2 is to the power-1 of the original number of power X
=12x
Derivative of 2x ^ 3 = 6x ^ 2
This is the formula of derivative
See?
Leave a message if you have any questions
6x2-12x: Why - 12x
Solving problems with the knowledge of greatest common factor and least common multiple
One day after the heavy snow, Tingting and her father started from the same point and measured the perimeter of a circular flower bed in the same direction. Tingting's step length was 54 cm, and dad's step length was 72 cm. Because their footprints overlapped, only 60 footprints were left on the snow. Q: how many meters is the perimeter of this flower bed?
The minimum common multiple of 54 and 72 is 216. So when Tingting walks 4 steps, his father walks 3 steps. That is to say, when Tingting walks 4 steps, his father walks 3 steps. There are only 4 + 3-1 = 6 footprints. There are 60 footprints in total. Tingting walks 40 steps, and his father walks 30 steps
Tingting is 54 cm long in each step, and dad is 72 cm long in each step
The least common multiple of 54 and 72 is 216
So when Tingting takes 4 steps, dad takes 3. It will overlap.
That is to say, Tingting takes 4 steps and dad takes 3. There are only 4 + 3-1 = 6 footprints.
A total of 60 footprints, which happened 10 times.
Tingting took 40 steps and Dad took 30. The perimeter of flower bed is 40x54 = 2160cm = 21.6m.
If it's just right, the last footprint should be spread out with the one who just started to stand
Tingting is 54 cm long in each step, and dad is 72 cm long in each step
The least common multiple of 54 and 72 is 216
So when Tingting takes 4 steps, dad takes 3. It will overlap.
That is to say, Tingting takes 4 steps and dad takes 3. There are only 4 + 3-1 = 6 footprints.
A total of 60 footprints, which happened 10 times.
Tingting took 40 steps and Dad took 30. The perimeter of flower bed is 40x54 = 2160cm = 21.6m.
[if it's just right, the last footprint should coincide with the place where you just started, so there's no need to consider the footprint at the beginning. Of course, the answer to this question should be the same. It's not necessary to put it away
The least common multiple of 54 and 72 is 216. So when Tingting takes 4 steps, dad takes 3 steps. It will overlap. That is to say, Tingting takes 4 steps and dad takes 3. There are only 4 + 3-1 = 6 footprints. A total of 60 footprints, which happened 10 times. Tingting took 40 steps and Dad took 30. The perimeter of flower bed is 40x54 = 2160cm = 21.6m
Tingting is 54 cm long in each step, and dad is 72 cm long in each step
The least common multiple of 54 and 72 is 216
So when Tingting takes 4 steps, dad takes 3. It will overlap.
That is to say, Tingting takes 4 steps and dad takes 3. There are only 4 + 3-1 = 6 footprints.
A total of 60 footprints, which happened 10 times.
Tingting took 40 steps and Dad took 30. The perimeter of flower bed is 40x54 = 2160cm = 21.6m. ... unfold
Tingting is 54 cm long in each step, and dad is 72 cm long in each step
The least common multiple of 54 and 72 is 216
So when Tingting takes 4 steps, dad takes 3. It will overlap.
That is to say, Tingting takes 4 steps and dad takes 3. There are only 4 + 3-1 = 6 footprints.
A total of 60 footprints, which happened 10 times.
Tingting took 40 steps and Dad took 30. The perimeter of flower bed is 40x54 = 2160cm = 21.6m. Put it away
Y = (x ^ 2 + 2x + 2) * f (e ^ - x), where f (x) has second derivative, find y“
Y '= (2x + 2) f (e ^ - x) - (X & # 178; + 2x + 2) (e ^ - x) f (e ^ - x) y' '= 2F (e ^ - x) - 2 (2x + 2) (e ^ - x) f (e ^ - x) + (X & # 178; + 2x + 2) (e ^ - x) f (e ^ - x) + (X & # 178; + 2x + 2) (e ^ - 2x) f (e ^ - x) hope to help you. If you have solved the problem, please click the "select as satisfactory answer" button below
It's too troublesome.
The greatest common factor of two numbers is 4 and the least common multiple is 252. If one number is 28, what is the other number?
252 △ 28 = 9, 4 × 9 = 36; a: another number is 36
According to the definition of derivative, find the derivative of function F X = x Λ 2 + 2x at point x = 2
f'(x)=2x+2
f'(2)=4+2=6
A △ B = 4. The greatest common factor of a and B is () and the least common multiple is ()
The sum of a and B is the greatest common factor
Derivative of y = Xe ^ x + 2x + 1
Y = Xe ^ x + 2x + 1
y'=e^x+xe^x+2=(x+1)e^x+2
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The greatest common factor and the least common multiple of 4 and 10
4=2*2
10=2*5
The greatest common factor of two numbers is 2
The least common multiple is 4 * 10 / 2 = 20
The greatest common factor is 2
The least common multiple is 20
The factor of 4 is 1, 2, 4.
The factors of 10 are 1,2,5,10.
As you can see from above, the greatest common factor of 4 and 10 is 2.
4 * 5 = 20, 10 * 2 = 20.
So their least common multiple is 20.
The greatest common factor of 4 and 10 is 2, and the least common multiple is 20
How to calculate the derivative of x power + 2x - 1 of y = Xe
X-Power of y = Xe + 2x - 1
y'=x'*e^x+x*(e^x)'+(2x)'+(-1)'
=e^x+x*e^x+2+0
=e^x+x*e^x+2
The method of finding the greatest common factor and the least common multiple of two numbers
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Greatest common factor
1、 Enumeration method: it is to write out all the factors of several numbers and find out the common factor - the greatest common factor through comparison, observation
Find (12,18)
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 18 are: 1, 2, 3, 6, 9, 18
The common factors of 12 and 18 are: 1, 2, 3 and 6
（12,18）=6
2、 Decomposing quality factor method: decomposing several numbers into quality factor form and multiplying the common factor to get the greatest common factor
Find (12,18)
12=2×2×3
18=2×3×3
（12,18）=2×3=6
2. The solution of the least common multiple
Common methods for finding the least common multiple of several numbers are as follows:
(1) To find the least common multiple of several numbers, first check whether these numbers have a common divisor (not necessarily the common divisor of all known numbers, but the common divisor of any two numbers). If there are any, use their common divisor to divide continuously until every two numbers are coprime numbers, and then multiply all divisors and the final quotient, The product is the least common multiple of these numbers
Example: ① find the least common multiple of 12 and 18
2 and 3 are coprime, except so far
The least common multiple of 12 and 18 is 2 × 3 × 2 × 3 = 36
② Finding the least common multiple of 12, 18 and 24
1. Every two numbers of 2 and 3 are coprime numbers, except so far
12. The least common multiple of 18 and 24 is 2 × 3 × 2 × 1 × 3 × 2 = 72
To find the least common multiple of two numbers, we can use the relationship between the two numbers and their greatest common divisor and least common multiple
The relation is: the greatest common divisor × the least common multiple = the product of multiplication of two numbers
Example: find the least common multiple of 12 and 18
Because the greatest common divisor of 12 and 18 is 6 and the product of the two numbers is 12 × 18 = 216, the least common multiple of 12 and 18 is 216 △ 6 = 36
(3) Direct observation
① The relationship between two numbers is multiple
If the larger number is a multiple of the smaller number, then the larger number is the least common multiple of the two numbers. For example: 96 is a multiple of 16, 96 is the least common multiple of 96 and 16
② The two numbers are coprime
If two numbers are coprime numbers, then the least common multiple of the two numbers is the product of the two numbers. For example, the least common multiple of 7 and 13 is 7 × 13 = 91
Short division
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