![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Let z = f (XZ, Z / y) determine the function of Z as X, y to find DZ
F record the partial derivative of the first variable as F1 and the partial derivative of the second variable as F2,
DZ = F1 * D (XZ) + F2 * D (Z / y)... [Note: if it is completely written, it is F1 (XZ, Z / y), and so is F2]
=f1*(xdz+zdx)+f2*(dz/y-zdy/y^2),
(1-xf1-f2/y)dz=zf1dx-(zf2/y^2)dy,
dz=[zf1dx-(zf2/y^2)dy]/(1-xf1-f2/y).
F (x, y, z) = x ^ 3Y ^ 2Z ^ 2, where Z is the implicit function determined by equation x ^ 3 + y ^ 3 + Z ^ 3-3xyz = 0. Try to find FX (- 1,0,1)
First, let (x, y, z) = x ^ 3 + y ^ 3 + Z ^ 3-3xyz
gx=3x^2-3yz gz=3z^2-3xy
zx=-(gx/gz)=-(3x^2-3yz)/(3z^2-3xy)=-(x^2-yz)/(z^2-xy)
Let's take the derivative of F (x, y, z) (in this case, y can be regarded as a constant and Z as a function of x)
fx=3x^2z^2+x^3*2z*zx
=3x^2z^2-x^3*2z(x^2-yz)/(z^2-xy)
Substitute (- 1,0,1)
FX = 3 * 1 * 2 * 1 - (- 1) * 2 * 1 / 1 = 8
If you want to ask high numbers, Given f (x, y, z) = 0; how to find the second derivative of Z to x? I know the first order is δ z/ δ x=-(Fx/Fz); How to use FX and FZ and FXX, fzz, fzx, FXZ to express the second partial derivative of Z to x? I don't understand how to calculate the partial derivative of this type of composite function. Please help me. Thank you now
δ ( δ z/ δ x)/ δ x==-([Fxx*Fz-Fzx*Fx]/(Fz)^2)
Others are similar
High number implicit function Y ^ y = X. determine that y is a function of X and find dy Is y to the power of Y·
Take logarithm on both sides:
So ylny = LNX
Take the derivative of X on both sides. Note that y is a function of X. taking the derivative of Y is essentially a derivative of a composite function
Then (ylny) '= (LNX)'
Y'lny + y × 1/y × y'=1/x
So (LNY + 1) × y'=1/x
So y '= 1 / [x (LNY + 1)]
Find the volume bottom radius of the cylinder is 3 and the height is 5
Hope naked oats,
three point one four × three × three × 5＝141.3
Given that the radius of the bottom surface of the cylinder is 3cm, the relationship between the volume y (cubic centimeter) and the height x (centimeter) of the cylinder is
Cylinder volume = bottom area × high
Bottom area = 3 ² π=9π
y=9π/X
RELATED INFORMATIONS
- 1. Then the functional relationship between the volume V (cm3) of the cylinder and the circumference C (CM) of the bottom surface? 1. (p4-12) let the height h (CM) of the cylinder be a constant, then the functional relationship between the volume V (cm3) of the cylinder and the circumference C (CM) of the bottom surface?
- 2. Given that the side area of the cone is a fixed value of 8 π, the analytical function and definition domain of the generatrix length L with respect to the bottom radius R are obtained
- 3. Y = 1 / x + √ (x) find the derivative
- 4. Beginners ask questions about the derivation rule of higher numbers Isn't there a formula called the derivative of the inverse function = 1 / (the derivative of the original function). If the original function = exponential function (based on e), then the inverse function = natural logarithm If the derivative of the inverse function = 1 / X and the derivative of the original function = e ^ x, then 1 / x = e ^ (- x) is contradictory,
- 5. (x + △ x) ^ 1 / 2-x ^ 1 / 2 derivation
- 6. Derivation rule: given f (x) = (1 + x ^ 2) arctanx, find f '(0)
- 7. Function f (x) = cos2x − 1 The period of 2 is （ ） A. π four B. π two C. 2π D. π
- 8. Derivative of integral? The integral is not only the original function of the derivative, but also the area surrounded by the original function and the X axis. Can we set the integral of function f (x) as G (x), and then take the derivative of G (x) to get the original function? Is g (x) a function of area s and independent variable x?
- 9. The 5th power of function ax + the 3rd power of BX + Cx. If f (- 7) = 7, what is f (7) = 5 F (- 7) = 7 indicates that f (- x) = f (x) should not be an even function
- 10. If the function y = e (A-1) x + 4x (x ∈ R) has an extreme point greater than zero, the range of real number a is () A. a＞-3 B. a＜-3 C. a＞−1 three D. a＜−1 three
- 11. High number: the square of the general solution of differential equation YY "+ 1 = y ', the answer is y' = P, Y" = PDP / P, and only / P / > 1, / P / 1, / P/
- 12. If x = 12 / π, how much is Cos4 to SiN4
- 13. The range of y = 1 / (x power of 3 + 1) is
- 14. If the power of X - the power of y = 30, x + y = 6 / 5, find the value of X-Y Hurry up, it's not that I don't use my brain, but that I still don't have an eyebrow after using my brain You kind and smart people. Solve it for me
- 15. Given that the domain of the function f (x) = LG (ax kbx) (k > 0, a > 1 > b > 0) is exactly (0, + ∞), is there such a, B that f (x) takes a positive value on (1, + ∞), and F (3) = LG4? If it exists, find the values of a and B; If not, please explain the reason
- 16. Find the differential of the root x power of E ∫ the root x power DX of E
- 17. The problem of integral variable substitution of univariate function? If it is such a question ∫ (the upper limit is positive infinity, the lower limit is 1) [1 / X √ (x-1)] DX, you can use √ (x-1) = t as a variable substitution But this question ∫ (the upper limit is positive infinity, the lower limit is 1)) [1 / X √ (x-1)] DX =? It is necessary to use x = 1 / T, but not √ (x square - 1) = t as in the above question, Why?
- 18. The sequence xn = (1 + 2) ^ (- 1) + (1 + 2 ^ 2) ^ (- 1) + (1 + 2 ^ 3) ^ (- 1) +... + (1 + 2 ^ n) ^ (- 1) proves that {xn} converges
- 19. A basic problem to prove the limit of sequence: LIM (n - > infinite) 3N / (n + 1) = 3... How to prove it? The answer is n = [(3 / x) - 1] x is any small positive number
- 20. Who can help The side length of the square ABCD is 2cm. P is a point on the CD. The extension line connecting AP and BC intersects point E. when point P moves on the side CD, the area of the triangle Abe changes 1. Let PD = xcm (0 < x ≤ 2), find the functional relationship between the area y and X of the triangle Abe 2. According to the functional relationship in 1, determine where the point P is a triangle and the area is 400cm ^ 2 The square ABCD is marked counterclockwise from the upper left corner, which seems to affect the topic