Let z = f (x ^ 2 + y ^ 2, XY), where f has a continuous partial derivative of the first order, and then find ᦉ 8706; Z / ᦉ 8706; X

The U = x ^ 2 + x ^ 2 + y ^ 2, v = 2, and we are going to be the U \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\v)

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1. Let f (x) be defined in (- ∞, + ∞), f (0) not equal to 0, f (XY) = f (x) f (y). It is proved that f (x) = 1
2. Higher number: find the partial derivative of function. Z = (1 + XY) ^ y,
3. Z = Z (x, y (Z, x)), for both sides of X partial derivative, &; Z / &; X can be eliminated The original problem, z = Z (x, y (Z, x)), and &; Z / &; y is not equal to 0, find &; Y / &; X The answer is as follows: take partial derivatives of X on both sides of the equation, and you will get 0 = &; Z / &; X + &; Z / &; y * &; Y / &; X I don't understand here
4. Let z = (x, y) be a function determined by F (X-Y, Y-Z, z-x) = 0, and let F 2 'not equal to f 3', try to find the partial derivative ᦉ 8706; Z / ᦉ 8706; X, ᦉ 8706; Z / ᦉ 8706; y
5. The partial derivative d ^ Z / DXDY of Z = f (XY, y)
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7. Finding the partial derivative of SiNx * e ^ XY
8. Finding the second order partial derivative of Z = XY + (x ^ 2) siny
9. We know that the function f (x) defined on the real number set is not always 0, and for any X. y belongs to R, satisfying XF (y) = YF (x), and judge the parity of F (x)
10. It is known that f (x) is a function defined on R which is not always zero, and for any x, y ∈ R, f (XY) = XF (y) + YF (x) The problem is if y = f (x) is an increasing function on [0, + ∞) and satisfies f (x) + F (x-1 / 2)
11. Let y = ln (XY) find the partial derivative ᦉ 8706; Z / ᦉ 8706; X
12. If the function z = ln (x + Y / 2x), then the partial derivative AZ / ay=
13. Let X / z = ln (Z / y), find AZ / ax, AZ / ay
14. Let z = f (x squared - y squared, XY), calculate AZ / ax, AZ / ay
15. If y = (x, z) is obtained from z = f (x, y), then does the partial derivative (AZ / ay) (ay / AZ) = 1 hold
16. Let z = f (XY, x ^ 2-y ^ 2), where f has the second order continuous partial derivative, find a ^ Z / ax ^ 2
17. The first and second partial derivatives of XYZ = x + y + Z I want to know more about it
18. Let y = y (x) be the implicit function determined by the functional equation E ^ (x + y) = 2 + X + 2Y at points (1, - 1), and find y "| (1, - 1) and Let y = y (x) be the implicit function determined by the functional equation E ^ (x + y) = 2 + X + 2Y at points (1, - 1), and find the quadratic differential of Y "| (1, - 1) and dy
19. What is the gradient of the function u = ln (x + y + Z) at point m (1,2, - 2)
20. Let f (x) and G (x), H (x) = max {f (x), G (x)}, u (x) = min {f (x), G (x)}. How to express H (x), u (x) with F (x), G (x)? Let f (x) and G (x) be continuous in the same interval, where H (x) = max {f (x), G (x)}, u (x) = min {f (x), G (x)}. How to express H (x), u (x) with F (x), G (x) and some operational symbols such as "+", "-"?