10. Show that if f is homogeneous of degree n, then r* fn + 2ryfzy + y° fy = n(n – 1)f(x, y). (A function f is called homogeneous of degree n if it satisfies the equation f(tx, ty) = t" f(x, y) for all t, where n is a positive integer and f has continuous second order partial derivatives).

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A: The solution are next step

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A: The answer is found in step-2

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A: Given: fx,y=x216y3-lny   As we know that; The Power law: ddxxn=nxn-1 And ddxlnx=1x

Q: 10. Show that if f is homogeneous of degree n, then a² fzz + 2ryfzy + y² fyy = n(n – 1)f(x, y). (A…

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Q: „2,3 - Let u = xʻy°, v = second order partial derivatives satisfying: f(4, 0) sin(rx), and z = f(u,…

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Q: a) z=x² In (x y²) b) z=4 cos(x-3y)

A: As we know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Chain rule:…

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A: Using the chain rule and rule of partial derivative and get the required derivative.Final solution…

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A: a) Ans: YES  b) Ans: NO

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A: find the partial derivative as following:-

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Q: 12.2.7. Suppose that Q := {(x, y) e R : x > 0 and y > 0} and that f is a continuous function on R?…

A: Sol

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Q: EXAMPLE 7 If z = f(x, y) has continuous second-order partial derivatives and x =r + s' and y = 2rs,…

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Q: 2. Suppose that f(x,y) is a continuous function of two variables such that each of the first and…

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Q: 9. Establish the fact, widely used in hydrodynamics, that if f(x, y, z) = 0, then A)), (E) - dz -1.…

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Q: Show that the mixed partial derivatives Fxyy, Fyxy, and Fyyx  of F(x,y,z) = 2z / (x+y) are/aren’t…

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Q: Suppose f(x, y) = ln(x^2 + y^2 ). A. Compute each of the following partial derivatives: (i) ∂f/∂x…

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A: "Since you have asked multiple question, as per our guidelines we will solve the first question for…

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Q: Here, g(x, y) = z = 9x(x, y) = gy(x, y) = + y2. Find the partial derivatives gx(x, y) and gy(x, y).…

A: Given function is g(x, y) = x2 + y2

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A: Given function is  f(x,y)=x2+3xy where  x=t3eu , y=2teu we have to find the partial derivatives…

Q: Let a differentiable function z = f(h²(x² + y3), 2łn(x +y)) satisfying the condition f(4,0) 1 be…

A: We need to find the partial derivative of z with respect to x for the given function.

Q: 1. Define G: R² R' by G(0,0) = 0 and G(x, y) = xy/(x² + y²)ž if (x, y) # (0,0). Show that G is…

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Q: 3. Evaluate all the first partial derivatives of the given functions at the given point. of of 1 a)…

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Q: (b) Show that the function f: R2 → R given by (* if (x, y) + 0, S(x, y) = 0 if (x, y) = (0, 0), is…

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Q: f(x, y) = In(0.82? + 0.8y²) a) Compute some partial derivatives. i) fe(x, y) : ii) fy(x, y) iii) fææ…

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Q: 9. The function f(x,y) = (xy)/(x² + 2y²) is_ at (0,0) and its partial derivatives %3D at (0,0) a.…

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Q: Show that the function ху si x? + y? + 0 f(x,y) = {x² +y² si (x.y) = (0,0) It has partial…

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Q: Find the first partial derivatives of the function. W = In(x + 3y + 6z) 1 x + 3y + 6z aw 3 ду х+ Зу…

A: Given :W=ln x+3y+6zTo determine∂w∂x,∂w∂y and ∂w∂z

Q: 21. If a function f: D→R is differentiable at a DED then f has partial derivatives fm and fu at (a,…

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Q: 0. Show that if f is homogeneous of degree n, then 1 fz + 2ryfry + y² fyy = n{n – 1)f(x, y). (A…

A: Let f be a homogeneous function of degree n and f has continuous second order partial derivatives.…

Q: 3. Consider the following function: = f(x, y) = et+2y (3x – y) (a) Calculate the first order partial…

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Q: 5. Show that the following functions ry (x² - y²) x² + y² (a) f(x, y) = 0, (b) f(x, y) = if (x² +…

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Q: #3. Find all the 2nd order partial derivatives for the given function h(x,y)=x*y2 - 4xy+e7y + In…

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Q: Find all the first order partial derivatives for the following function. f(x, y, z) = af af yz af 1…

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