Why is the derivative of F (x) = 2F (2-x) f '(x) = 2F' (2-x) * (2-x) ' Why is the derivative of F (x) = 2F (2-x) f '(x) = 2F' (2-x) * (2-x) '

Why is the derivative of F (x) = 2F (2-x) f '(x) = 2F' (2-x) * (2-x) ' Why is the derivative of F (x) = 2F (2-x) f '(x) = 2F' (2-x) * (2-x) '

Suppose f (x) = 2F (U), u = 2-x; then the original function is a composite function, and the derivation rule of composite function is to seek the derivative layer by layer and then make the product. In this way, f '(x) = 2F' (U) * (U) ', and then u = 2-x is f' (x) = 2F '(2-x) * (2-x)'
This is a composite function. The derivative of the composite function is the derivative of the inner function multiplied by the derivative of the outer function, so it will be multiplied by (2-x)`
If you have any questions, please ask. Thank you
This is the derivation of a composite function
First of all, if the problem we solve is relatively simple, for example, the derivative of y = X-2, we can directly solve it as 1
For compound functions, if you want to solve the problem of derivation, the rule is to first derive the whole, and then the part in brackets. You can multiply the two
That is to say, we first obtain 2F '(2-x) from the whole, and then we obtain the derivative from the inner part of the bracket, that is, (2-x)' by multiplying the two
This is the derivation of a composite function
First of all, if the problem we solve is relatively simple, for example, the derivative of y = X-2, we can directly solve it as 1
For compound functions, if you want to solve the problem of derivation, the rule is to first derive the whole, and then the part in brackets. You can multiply the two
That is to say, 2f '(2-x) is derived from the whole, and then (2-x)' is derived from the inner part of the bracket
Urgently seeking the derivative of F (x) = 2x + 2xinx / X Λ 2-1
It's urgent today,
(x Λ 2-1) is bracketed
(x Λ 2-1) is also bracketed, and the derivative of (x Λ 2-1) is 2x
I think the X in the middle of your 2xinx should be a multiplier sign, or it should be divided with the denominator
F '(x) = 2 + [2 / X * (x ^ 2-1) - 2lnx * (2x)] / (x Λ 2-1) ^ 2, just simplify it
The derivative of the first term of X is a number, and the derivative of the 0-th term of X (i.e. the constant term) is 0. Only the middle term is troublesome. The numerator denominator has x, and the fraction derivation formula: (V / U) '= (V' * U-V * u ') / u ^ 2
Let 2x = a, 2xinx / x ^ 2 = B
The derivative of a is a '= 2
B = 2xinx / x ^ 2 = 2inx / X
b'=（2Inx/x）'=2[（Inx）'*1/x+Inx*(1/x)']=2[1/(x^2)-Inx*(1/(x^2))]
f'(x)=a'+b'
F (x) = 2x, find the derivative of F (1 + x ^ 2)
This kind of problem should be derivative or substitution first? In fact, it's because doing a similar problem is derivative and substitution first, but I'm confused when I move to this problem
1] Derivation of composite function: [f (1 + x ^ 2)] '= f' (1 + x ^ 2) * 2x
2]f(1+x^2)＝2（1+x^2)＝2+2x^2=>[f(1+x^2)]'=4x
Because f (x) has a concrete expression, the method is more reasonable;
Let g (x) = 1 + x ^ 2
f′(g(x))=2x×g′(x)+2×g(x)
Look at the meaning of the problem, this problem should be replaced and then derivative, that is, compound function derivative
Find the derivative dy / DX of the implicit function to x determined by ∫ (0 to y) e ^ XDT + ∫ (0 to x) cost DT = 0? You can help to solve it
e^y*y'+cosx=0
y'=-cosx/e^y
If the natural number a is 6 times of B, then the least common multiple of a and B is______ The greatest common divisor is______ .
A is 6 times of B, a is bigger than B, the least common multiple of a and B is a, the greatest common factor is B, so the answer is: A, B
Let z = x ^ 2-y ^ 2, x = Sint, y = cost, find DZ / dt
A △ B = 5 (both a and B are natural numbers), then the greatest common divisor of a and B is (), and the least common multiple is ()
The greatest common divisor of a and B is (b), and the least common multiple is (a)
The greatest common divisor is B and the least common multiple is a.
The greatest common divisor is B and the least common multiple is a.
If there is a natural number a divisible by natural number B, then a is called a multiple of B and B is a divisor of A. The common divisor of several natural numbers is called the common divisor of these natural numbers. The greatest common divisor in the common divisor is called the greatest common divisor of these natural numbers.
Least common multiple (abbreviated as l.c.m.), if there is a natural number a which can be divided by natural number B, then a is called multiple of B, and B is the divisor of A. for two integers, it means that the two numbers are expanded together
The greatest common divisor is B and the least common multiple is a.
If there is a natural number a divisible by natural number B, then a is called a multiple of B and B is a divisor of A. The common divisor of several natural numbers is called the common divisor of these natural numbers. The greatest common divisor in the common divisor is called the greatest common divisor of these natural numbers.
Least common multiple (abbreviated as l.c.m.), if there is a natural number a which can be divided by the natural number B, then a is called the multiple of B, and B is the divisor of A. for two integers, it refers to the smallest common multiple of the two numbers. When calculating the least common multiple, the maximum convention number is usually used to assist the calculation. Where 4 is the least common multiple, called their least common multiple. For example, when the ten day Gan and the twelve earth branches are called a lunar year, the time required for the circulation of the GaN and Zhi to return to the same name is the least common multiple of 12 and 10, which is 60 - a "Jiazi". When adding and subtracting fractions, the denominator of two numbers must be the same, so it is necessary to divide them. If the denominator of two fractions is divided into the least common multiple, the amount of calculation will be the lowest. Put it away
The greatest common divisor is (b) and the least common multiple is (a).
Since a is a multiple of B, then the greatest common divisor is (b) and the least common multiple is (a). It has nothing to do with the number 5. No matter how much a / b equals, that's the answer.
Let z = x2y2, where x = Sint, y = cost, find DZ / dt
2 is the power of two
This problem belongs to the derivative category of compound function!
The detailed process is as follows:
dz/dt
=(x^2)'y^2+x^2(y^2)'
=2sint(cost)^3-(sint)^3*2cost
=2sintcost[(cost)^2-(sint)^2]
=sin2tcos2t
=(1/2)*sin4t
z=x^2*y^2=(1/4)(sin2t)^2
dz/dt=(1/4)*2sin2t*cos2t*2
=(1/2)sin4t
Z=（sint）^2(cost)^2
=1/4(sin2t)^2
=1/4*1/2(1-cos4t)
=1/8-1/8cos4t
dz/dt=1/8*4sin4t=1/2sin4t
If Ba = C (a, B, C are all natural numbers not equal to 0), the greatest common factor of a and B is______ The least common multiple is______ .
From the meaning of the question, B △ a = C (a, B, C are not equal to 0 of the natural number), we know that B is a multiple of a, so the greatest common factor of a and B is a, the least common multiple is B; so the answer is: a, B
How to find the second derivative of y = Xe ^ x ^ 2?
Unfortunately, the answers upstairs are all wrong
Unfortunately, my picture is full. It can't be uploaded until daybreak
The answer to this question is & nbsp; = (2x & amp; sup2; + 2x + 1) e ^ X & amp; sup2;