What is the derivative of F (x) = INX + X + 2 / x? Mainly INX

What is the derivative of F (x) = INX + X + 2 / x? Mainly INX

g(x)=lnx g'(x)=1/x
f'(x)=1/x+1-2/x^2
f'(x)=1/x + 1 - 2/x^2
(lnx)'=1/x, f'(x)=1/x-2/x^2=(x-2)/x^2
If a > b > 0, what is the minimum value of the algebraic formula A ^ 2 + 1 / b (a-b)?
The application of mean value theorem
Because a > b > 0, B (a-b) = a ^ 2 + 4 / A ^ 2 > = 2 * √ (a ^ 2 * 4 / A ^ 2) = 4,
When B = A-B and a ^ 2 = 4 / A ^ 2, i.e. a = √ 2, B = √ 2 / 2, the minimum value is 4
It's better to ask the math teacher directly You can't be in the exam
How to find the derivative of F (x) = a (inx-x)
f'(x)=a(1/x-1)
What is the minimum value of the algebraic formula A ^ 2-2ab + B ^ 2-10? When the algebraic formula gets the minimum value, what conditions should a and B satisfy
solution
a²-2ab+b²-10
=(a-b)²-10
≥-10
When a = B, the minimum value is - 10
Because a ^ 2-2ab + B ^ 2-10 = (a-b) ^ 2-10 ≥ - 10,
So the minimum value of the algebraic formula A ^ 2-2ab + B ^ 2-10 is - 10; in this case, a = B
1.f(x)=x(x^2+1/x+1/x^3) 2.f(x)=(e^x+Inx)/x 3.f(x)=sinx(cosx+2^x) 4.f(x)=5log2(2x+1)
1.f(x)=x(x^2+1/x+1/x^3) =x^3+1+1/x^3f'(x)=3x^2-(1/3)/x^42.f(x)=(e^x+Inx)/xf'(x)=[(e^x+Inx)'+(e^x+Inx)x]/x^2 =(e^x+1/x+xe^x+xInx)/x^2=(x^2*e^x+xe^x+x^2*lnx+1)/x^#3.f(x)=sinx(cosx+2^x) f'(x)= (sinx)'(co...
P = 2A ^ 2-8ab + 17b ^ 2-16a-4b + 2073, when a and B are the values, P has the minimum value
Let the second derivative of F (x) exist and find the second derivative of y = f (INX)
Y '= [f (LNX)]' = f '(LNX) * (LNX)' = f '(LNX) / XY "= (y') '= [f' (LNX) / x] '= {[f' (LNX)] '* x - (x)' f '(LNX)} / (x ^ 2) = [f" (LNX) * (LNX)' * x - f '(LNX)] / (x ^ 2) = [f "(LNX) - f' (LNX)] / (x ^ 2) compound function derivation, it's OK to be familiar with intermediate variables
y'=f'(lnx)/x
y''=f''(lnx)/x^2-f'(lnx)/x^2
How simple is the derivation in brackets and then the derivation again
y'=f'(lnx)/x
y''=f''(lnx)/x^2-f'(lnx)/x^2
Y = 2A & # 178; - 8ab + 17b & # 178; - 16a-4b + 2068
Y = 2A & # 178; - 8ab + 17b & # 178; - 16a-4b + 2068 = (A & # 178; - 16A + 64) + (A & # 178; - 8ab + 16b & # 178;) + (B & # 178; - 4B + 4) + 2000 = (A-8) & # 178; + (a-4b) & # 178; + (b-2) & # 178; + 2000 ≥ 2000, y minimum = 2000
How to find the derivative of F (x) = x | x-a | + 2x
When x is greater than or equal to a, f '(x) = 2x-a + 2;
When x is less than a, f '(x) = - 2x + A + 2
Simply compare X and a, then segment
Given y = 2A ^ - 8ab + 17b ^ - 16A - 4B + 206B, find the minimum value of Y and the ATB value at this time
y=(a²-8ab+16b²)+(a²-16a+64)+(b²-4b+4)+138
=(a-4b)²+(a-8)²+(b-2)²+138
The least square is 0
If a-4b = 0, A-8 = 0, B-2 = 0 hold simultaneously
There is a minimum
In this case, a = 8 and B = 2 can be taken as 0 at the same time
So the minimum value = 0 + 0 + 0 + 138 = 138
a=8,b=2
The problem that has been solved is reproduced to QQ space. Y = 2A ^ 2-8ab + 17b ^ 2-16a-4b + 2066. What is the minimum value of Y? What are the values of a and B at this time?
[tag: known, minimum, known, minimum] answer: 3 popularity: 3 solution time: 2009-07-16 17:26
The minimum y is 1998 a = 8 B = 2
Perfect the answer
To unfold
The problem that has been solved is reproduced to QQ space. Y = 2A ^ 2-8ab + 17b ^ 2-16a-4b + 2066. What is the minimum value of Y? What are the values of a and B at this time?
[tag: known, minimum, known, minimum] answer: 3 popularity: 3 solution time: 2009-07-16 17:26
The minimum y is 1998 a = 8 B = 2
Perfect the answer
The adoption rate of the answers from the Holy Buddha: 5.9% 2009-07-16 17:05 improve the quality of asking, join the evaluation plan of satisfactory answers, and have prizes to evaluate the answers every day
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Satisfactory answer y = (a-4b) ^ 2 + (A-8) ^ 2 + (b-2) ^ 2 + 1998
When a = 8 and B = 2, the first three square terms are all equal to 0, which is called "collapse"