Verify that the conclusion of Clairaut's theorem holds, that is, Uxy = Uyx" u = x5y8 - y5 With u = x5y8y5, we have the following. 5x4 U xy = Uyx = "y=40x4₂7 40x¹y7 = 8x5y7 - 5y4 × Since u xy X = U Clairaut's theorem holds for u = x5y8-y5. 'yx'

Q: J32 For z = cos(x-4y) show that # дудхду 332 дугах

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Q: 8. Find all values of h, if any exist, such that b a linear combination of vị an h (а) Vi V2 = b =…

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Q: 2.,3 2) Find fx and fy if f(x, y) = 2x²y³ – 3xy² + 2x² + 3y² + 1

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Q: C = 3. 3. Find AB and BA given 3 A = and B = -7 -4 -2

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Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: 2 a) y = Find y'. 3e (ax-5)4

A: Explanation and solutions is given below.....

Q: d) Let g(x,y) = (3x + y)2(2y + 1) and h(x, y) = 6y2(2x + y) h i) Find дх’ ду’ дх’ ду

A: The given functions are  and

Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

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Q: If find az/au and az/av. дz/?u = Əz/dv= z = xe", x=u³v³, y=u³+v³₂ (In your answers, do not rewrite…

A: z=xeyx=u3-v3y=u3+v3from chain rule ∂z∂u=∂z∂x×∂x∂u+∂z∂y×∂y∂u

Q: Suppose u = (4, 1, 1) and v = (–4, −1, −3). Then: u + v= Ա υ V= u= 2u= -1/v= 7u - 6v=

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