(4) If z = f(x, y), where x=rcos and y = r sin 0, find the following дz дz (b) (c) show that ar dz Ər 2 + 1 p2 дz 2 = дz Әт 2 + дz ду 2

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Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

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Q: 2 Suppose that A = 3xyz²7 + 2xy³j - x²yzk and p = 3x² - yz. Find, at the point (1,-1, 1), 2.1 Vo,…

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Q: Find G'(w) if G(w) = 9 6 4w +6+ √w.

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Q: If fe F- di = Scl-5x + 4y) da + (a*y) dy, what is F? F =

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Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

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Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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Q: 15. Differentiate 4y³ with respect to x. A) 12y? B) 12y C) 12y2 dy D) 4y2 dy dx dx 16-17. Find the…

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Q: . Find, from first principles, f(2, -1) for f(x, y) = 2a?y³ + e2y. ,2,,3

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Q: The function u(x, y) obeys, 8²u Ərəy = -2e

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Q: Q111f и %3D (1 —2ху + у?)""/2, Prove that: ди ди y əx y? u3 У ду

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Q: Find Vf(a), given the following data. Calculate 91, 92 and g3 such that Vƒ(a): 91 92 93 = || || = 91…

A: The given problem is to find the grad f for the given data of directional derivative of function f…

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: f(x.y) = x³y – . Calculate Se af and əx ду

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Q: Determine the vesulting equaton Determine the vesulting equaton after using the suitable…

A: We have to find

Q: 2. +x +1 d

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Q: 9) y = e4x² + x A) dy dx 8xe2x + 1 B) dy - 8xex2 dx %3D + 1 C) dy dy - 8xe4x2 dx — 8хе + 1 %D D) + 1

A: We have to find

Q: af , Given the function f (x,y) = 3x – x²y² + 2x°y, what is iTe ду А. 3 — 2ху? + бх?у В. - 2х3у +…

A: Given query is to find the partial derivative with respect to y.

Q: Find r'(t), r"(t), r'(t) ・r"(t), and r'(t) × r"(t). r(t) = 클레 - 3tj + (a) r'(t) (b) r"(t) (c)…

A: We need to find derivative and dot and cross products.

Q: af Find and f(x, y) = 4xy – 6x? – y? + 9x – 3y + 3 - af af dy 3 f(x, y) = (4x – 6y)* fe af dy ||

A: Partially differentiate with respect to x and y. Detailed solution is given below.

Q: f of If dx + In(7y), what is ? - дхду Select one: 1 7. а. дхду y y b. дхду - y + 7e?y С. дхду 1+e7y…

A: Option E is correct.  Make x constant

Q: If f(x, y) = x³y + 9xy“, find the following. f(x, у) əx? |(1, 1)

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