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

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• 1. Higher number: find the partial derivative of function. Z = (1 + XY) ^ y,
• 2. 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
• 3. 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
• 4. The partial derivative d ^ Z / DXDY of Z = f (XY, y)
• 5. Z = arcsin (XY) to find the second derivative of this function There are four answers, two of which are equal
• 6. Finding the partial derivative of SiNx * e ^ XY
• 7. Finding the second order partial derivative of Z = XY + (x ^ 2) siny
• 8. 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)
• 9. 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)
• 10. It is known that f (x) is a function defined on R which is not always zero. For any x, y ∈ R, f (x · y) = XF (y) + YF (x) holds. & nbsp; sequence {an} satisfies an = f (2n) (n ∈ n *), and A1 = 2. Then the general term formula of sequence an=______ ．
• 11. 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
• 12. Let y = ln (XY) find the partial derivative ᦉ 8706; Z / ᦉ 8706; X
• 13. If the function z = ln (x + Y / 2x), then the partial derivative AZ / ay=
• 14. Let X / z = ln (Z / y), find AZ / ax, AZ / ay
• 15. Let z = f (x squared - y squared, XY), calculate AZ / ax, AZ / ay
• 16. If y = (x, z) is obtained from z = f (x, y), then does the partial derivative (AZ / ay) (ay / AZ) = 1 hold
• 17. Let z = f (XY, x ^ 2-y ^ 2), where f has the second order continuous partial derivative, find a ^ Z / ax ^ 2
• 18. The first and second partial derivatives of XYZ = x + y + Z I want to know more about it
• 19. 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
• 20. What is the gradient of the function u = ln (x + y + Z) at point m (1,2, - 2)