1. F(г, у) (x+ y)i+ ( – y) j - 2. F(x, y) = (x – y) i+ (x + y)j - 3. F(x, у) yi+ cos x j 4. F(x, у) 2i+ xj 5. F(x, у) (2x + 2) i+ yj

Q: If f(x,y,z)=xe^{4y}\sin(6z), then the gradient is

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Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

Q: 4.1 In aerodynamics and fluid mechanics, the functions u(x,y) and v(x,y) in f(z) = u(x,y) + iv(x,y),…

A: As per the policy, we are solving the first question. Please repost the question and specify which…

Q: 1. Find the first and second partial derivatives (that is f, af, , , and ) of Əx' dy' dx², ay² »…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: 4.1 In aerodynamics and fluid mechanics, the functions u(x, y) and v(x, y) in f(2) where f(z) is…

A: We will find out the required values.

Q: f(x, y) = /2x – y /2х — у f(x, y) = In(9 – x² – 9y²) f(x, y) = /1 – x²? - VI – y² S(x, y) = Vy + /25…

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Q: . Suppose that your best friend has calculated the partial derivatives of a given function f(x,y)…

A: Please see the below picture for detailed solution for detailed solution.

Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

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Q: In Exercises 5-8, calculate the gradient.

A: Here given as

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

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Q: 23. Find the most general antiderivative of the functions: a) f(x) = 1 –- x³ + 5x5 – 3x7. 5 – 4.x3 +…

A: Given: 1.fx=1-x3+5x5-3x7 2.g(x)=5-4x3+3x6x6 we want to calculate the antiderivative is nothing but…

Q: Suppose z = f(x,y) is a differentiable function of two variables. What do the partial derivatives,…

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Q: (a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y =…

A: Match the graph with their parametric equations.

Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

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Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: azz 2. A. If z = sin(3x+2y) , verify that 2 - 3 a2z = -6z ay2 B. If f = x³y³ + 2xcosy + y² lnx then…

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Q: A) F(x, y) = (x sin(x² + y²), ysin(x² + y²)) xy B) F(x, y) = x/y² + 1 y² + 1 C) F(x, y) = (yecos(=),…

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Q: sen (y) 1² + 3y? 522 – f(x, y) 2y – z 1² + 2y? f(z, y) zy3 12 + 2y? f(x, y) f(z, y) z°(1 – cos(y))…

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Q: 2. IShow, using the definition of the derivative, that the function f(x, y) differentiable at every…

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Q: 1) F(x, y, 2) = 3xyi + 2yz j+ 7xz k. 3) F(x, y, z) = 6 e" senyi + 2e* cos yj + 9z k. 5) F(x, y, z) =…

A: We will find out the required value .

Q: 1. f(x, y) = x2 + y² –1 2. f(x,y)= 3. f(x, y)= Vx+ y² +4 5. f(x, y)= In(xy) 7. f(x, y,z)= sin(xyz)…

A: Vf(x,y) =[d/dx(f(x,y) ,d/dy(f(x,y)]

Q: 9. Differentiate: а. f(x) 3D (2x? - 6х + 3)(3 — 5x%) 4- 3x – x? b. g(x) = x2 - 1 c. h(x) = x+5,3…

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Q: 7. f(x) = x² In x, f"'(x) 1 8. y = -, y" 1 .f"(q) 9. f(q) = 2g* 10. f(x) = /x, f"(x) 11. f(r) = /9 –…

A: The objective of the question is determine the derivative of the given function "y".

Q: 6. If V(x, y) = xsin x cos y + y² then, F-VV and it is equal to A. -ily sinx cos y sinx cos y]…

A: We can solve using divergence formula

Q: 4) Find f, fy and f, for the following i) f(x,y,z) = sin-xyz ii) f(x, y,z) = y z In xy iii) f(x,y,z)…

A: Note:  Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Let f(x, y, z) = 4xy – z², x = 6r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

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Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

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Q: sin(xz – 1) In(6+ 3xz + 4yz) = 0 determines z as function of x and y in a neighbourhood of the point…

A: Claim: at (x,y)=(1,1) for the equation  Take partial derivative with respect to x Substitute…

Q: (a) The function z depends on u and v so that z = (2u – 1)(1 –v)? , u = x + 2y and v = x – 2y az…

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Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: The equations xe" + uz – cos(v) – 2 = 0 and ucos(y) + 6x²v – 4yz² – 1 = 0 can be solved for (u,v) as…

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Q: At what points (x, y) in the plane are the functions in Exercises 31–34 continuous?

A: Since you have asked multiple question, we will solve the first two question for you. If you want…

Q: Example H-W:_for f(x,y) = cos(xy) – x³ + y* compute fxyy, fxxyy %3D

A: We have to find the partial derivative

Q: In Exercises 9-20, use the Chain Rule to calculate - f(r(t)) at the value dt of t given.

A: NOTE : As per Bartleby guidelines, incase of multiple questions only one will be answered. Please…

Q: If f(x, y) = 3 sin(2x +y)- 4 cos(x - y) then the second derivative fee is a. -12 sin(2x +y) +4 cos(z…

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Q: ecos a tan(z+ x) 2x – y+ z V4x2 + y – z xyz T T T x + 2y + 3z 3x + 4y – 2z, x + y + z

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Q: 2. Suppose that f (x,y) is a function so that f(x, 1) = e*- 3x + 2 f(0,y) = y2 +2y Find the partial…

A: We use the definition of partial derivatives to find the partial derivatives.

Q: A) F(x,y) = (cos(x+ y) – y sin(x + y), –x sin(x + y)) 1 2т — у B) F(x, y) = ( - x – y’ xy – y² C)…

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Q: Consider i = (1,0,0), j= (0, 1, 0), k = (0,0, 1) and, f (x, y) = (x, ²y°, sin x, cos y, xyean +3…

A: We have to make the appropriate selection  With the help of following transformation-

Q: 1. A force of F (x) 2x = xe + 6x – 2 acts on an object. What is the work required to move the object…

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Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: 1. f (x, y, z) = x° ỹ + 4z°y² – xyz + x² – Vz -

A: Given that: f(x, y, z)=x3y+4z3y2-xyz+x2-z53               NOTE: As per our answering guidelines, we…

Q: Find a general solution to (x' +xy')y' = y implict form F(x, y)= C : Give an

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Q: 30. y = 120 8. s -2+ 29. y =-- 10. y = 4- 2x-x 12 4 Sx 31. y (x- 1)(x + 3x - 5) 32. y = (4x' +…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

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Q: (b) Form the partial equation by eliminating function f from z = f(x?

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Q: Evaluate xsec¬xdx using integration by parts. OA x2 -sec-1x-(x² – 1)3/2+c 2 O B. x? 1/2 2 Oc x2…

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