fa(x(s, t), y(s, t)) = | f:(x(s, t), y(s, t)) -

Q: (xy(x²-y²) Let f(x, y) =} (x²+y²) (x, y) ± (0,0)| show that fxy (0,0) + f yx(0,0) (x, y) = (0,0)

A: This question is taken from the partial derivative in which we have to prove the given statement. We…

Q: 2² – 5y? Then y² + 2z2 Let f(x, y, z) = fz(æ, y, z)= | fy(æ, y, z)= | f:(x, y, z)=

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Q: ху f(x,y,z) =- х+у+z

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Q: f(x, y, z) = x – Vy² + z

A: Take the partial derivative ony by one with respect to x, y & z considering other as constant at…

Q: Calculate ∬Sf(x,y,z)dS For x^2+y^2=9,0≤z≤3;f(x,y,z)=e^(−z) ∬Sf(x,y,z)dS= ?

A: Find the parametric equation for the given curves.

Q: Find fr, fy, and fz. f (x, Y, z) = z In(x°y²cos(52)) fa = fy = fz = ||

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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: Given f(x, y, z) = v- 5x – 3y – 4z, find fa(x, Y, z) = f,(x, y, z) = f:(x, y, z) =

A: Given,          fx,y,z=-5x-3y-4z

Q: f(x, y, z) = 3x²y - 5xyz + 7yz2 2. f,(x, y, z) = f,xx, y, z) = f(x, y, z) =

A: Given query is to find the partial derivative for the given function f(x,y,z).

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: 37. f(x,y) = 9-x² – 7y³; f.(3, 1), fy(3, 1)

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

Q: (x* + y° ) In (x² + y* ). (x,y)= (0,0) f(x, y) = k +1, (x, y) = (0,0)

A: If f is continuous then lim (x, y) tends to (0, 0) =k+1 And using l hospital rule.

Q: Find Cx(x,y) if Cx(x,y) = 2x2 + 7xy - 9y2 + 4x - 9y - 6 Cx(x,y) = ?

A: Let's find.

Q: Given f(x, y, z) = x³yz². Find f.(1,1,1).

A: The equation we have , f(x,y,z) = x3yz2 We have to find out fz, Now we differentiate f(x,y,z) with…

Q: f(x, y) = (-x – 2y, x – 4y).

A: Follow the steps.

Q: :f (x, y, 2) = x + y; E = {(x, y, z) |1 0, y > 0}

A: In this question given that a function and it is in the cartetion coordinate. We can convert in…

Q: f(x,y) = x² + 3xy +y² fonksiyonu için fex (2,3)]. [fyy (2,3)] – Fzy (2,3)]? =

A: The answer is, (-5) The detailed solution is as follows below :

Q: F = [r. -x, 0]. = [y. -X, S: 3r + 2y + := 6, x2 0, v 2 0, z 2 0

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Q: valuate S. F · ds, where F(x, y, z) = (z, x, y) and c(t) = (t, t², t³), 0 < t < 1.

A: F(x,y,z)=(z,x,y)

Q: af (x,y) f(x, y)=xe"+* 5 у, Х (а) Сompute y af(x,y) X f(x, y)=xe³"+* ,5 у (b) Compute ду y

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Q: u = x² + y³ + z*, X = s•t = s2 +t2 y = z = s-t

A: We find complex function

Q: A) f(x,y,z) = 2x + y – z , Q = {(x, y, z): 0 < x, z < 2,-2 < y< 2}

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

Q: (c) Ã = xẽ, + yếy, C : {n² + y² = 1, z = 0} %3| ex (d) Ā = En + Ey 2 + 12 C : {y = x, z = 0, x € (0,…

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Q: If F(x,y,z)=x?y-y²z3 Then fz= -3y²z2

A: Given: fx, y, z=x2y3-y2z3

Q: Given f(x,y,z)=√(−6x+5y+2z), find fx(x,y,z) = fy(x,y,z) = fz(x,y,z)=

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Q: Given f(2, y, z) =v V-I - 2y + z, find f.(z, y, z) = f(z, y, z) = f(1, y, z) =

A: We will use definition of differentiation. First we will handle derivative of the root of the…

Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

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Q: (xy(x²–y²) f(x, y) = { (x²+y²) (x, y) # (0,0) (x, y) = (0,0) ) show that fxy(0,0) f yx(0,0) Let

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Q: 2² – 6y? Then Let f(x, y, z) y2 + 4z² fz(x,y, z)= fy(x, y, z)= f-(x, Y, z)=

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Q: f(x, y, z) = 2 ≤ x ≤ 10,0 ≤ y ≤ 4,0 ≤ z ≤4

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Q: If f(x.y,z)= y + xz then f ,(1,1,1) =

A: The given function is  f(x, y, z) = y5 + xz

Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

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Q: 2. Evaluateſff, y dV, where: E = {(x,y,z)|0 <x< 1,0 < y < 4x,y < z < x² + y} %3D

A: The solution are next step

Q: Calculate fw(-1, 2, 0, –1) where f(x, y, z, w) = xy²z – xw² – e2a²-v²-²+2w²

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Q: ху af If f(x,y) then is %3D x2+y ax

A: Given function,  fx,y=xyx2+y

Q: What is the antiderative of xysin((x^2)y)?

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Q: Display the values of the functions in Exercises 37–48 in two ways:(a) by sketching the surface z =…

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Q: f (x, y, z) = x² + y² + z² and u = (1,0, 1) at P(1, 1, 1).

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Q: f(x, y) = e&z– 4y af af ду

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Q: Consider f (x, y) = re63ry f-(x, y) = e63ry and fy(x, y) = %3D e63ry

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Q: Given f(x, y, z) = V5x – 5y + 2z, find fa(x, y, z) =| %3D fy(x, y, z) = f-(x, y, z) =|

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Q: f(x, y, z) = 4x²y - 2xyz + 9yz2 (X, y, z) = ,(x, y, z) = f_(x, y, z) =

A: Answer and explanations is given below...

Q: Is F(x,y)= (2²y,5– zy²) source free?

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Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

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Q: If F(x,y, z) = (5x – y + az)î + (bx + 2y + 5z)ĵ + (2x + cy – z)k is irrotational then find the value…

A: Explanation of the answer is as follows

Q: f(x, y, z) = 4x²y - 8xyz + 10yz? (x, y, z) = %3D x. Y. z) = f,(x, y, z) =

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Q: [f(x)dx, if f(x) = Vx -k+1;k-13x <k,k = 1, 2,..

A: