Find fy, fy, and f, and evaluate each at the given point. ху fx, у, 2) (8, 1, –1) x + y + z f,(x, y, z) = f,(x, y, z) f,(x, y, z) = f,(8, 1, -1) = f,(8, 1, –1) = f,(8, 1, -1) =

Q: Find g(u(x, y), v(x, y)) if g(x, y) =ysin(x2y), u(x, y) =x2y3 and v(x,y)=πxy.

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Q: Let Ms, 0 = Rus, (), Ms. 0), where F, u, and v are differentiable, and the following applies. u(6,…

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Q: Find x; y; z; t where 3 (, ) = (_; )+(,÷, **) 6 4 x + y\ \z +t 1. O x = 2,y = 4,z = 2,t = 3 2. O x =…

A: Find x,y,z,t

Q: Find fx, fy, and fz, and evaluate each at the given point. f(x, y, z) = x2y3 + 2xyz − 6yz,    (−3,…

A: To determine the partial derivatives of given function at point (-3, 1, 3).

Q: z = f(st - 3, s2 +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9) =…

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Q: Find fx, fy, and fz, and evaluate each at the given point. f(x, y, z) = x2y3 + 2xyz − 7yz, (−3,…

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Q: Let f(x, y, z) = xy²z³ + 3 find i)f(2, 1, 3) ii)f(t, t², -t) iii)f(a + b, a – b, b)

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

Q: Find f, and f, and evaluate each at the given point. 8хy f(x, y) = V3x2 (1, 1) + 6y2 fy(x, y) =…

A: Answer is given below

Q: Compute f, aL a2f and :f(x, y) = (x + y)(2x + y)² ax' ay дхду

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Q: Find fx fy, and f₂, and evaluate each at the given point. f(x, y, z) = x²y³ + 2xyz - 7yz, (-3, 1, 3)…

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Q: Find fx, fy, and f, and evaluate each at the given point. f(x, y, z) = x²y³ + 2xyz - 6yz, (-3, 1, 3)…

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Q: Let W(s,t) F(u(s, t), v(s, t)) where u(1,0)-4, u,(1,0) 3, u(1,0)- 5 v(1,0) 7, v.(1,0)=-3, v(1,0)--6…

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Q: Determine whether the statement is true or false. If (3, 8) is a critical point of f and fyo(3,…

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Q: Find fy, fy and f,, and evaluate each at the given point. X''y' z' fx, у, 2) %3D х*уз + 2хyz - 4yz,…

A: We have to find derivative

Q: x = x(u, v), x(-1, 5) = 1 and y(-1,5) = 4, calculate z, (-1,5) in terms of some of the Given z =…

A: Please see the below picture for detailed solution.

Q: Find f, f, and f, and evaluate each at the given point. f(x, y, z) = x²y + 2xyz - 8yz, (-3, 1, 3)…

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Q: 6. Let u = (p^2-q)/(q-r^2), where p= x^2-y+z, q = x- y+ z^2, and r = x+ y -Z. %3D Find ôu/ôy at the…

A: Given that, u=p2-qq-r2 p=x2-y+zq=x-y+z2r=x+y-z ⇒u=(x2-y+z)2-(x-y+z2)(x-y+z2)-(x+y-z)2

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the fol u(-3, 6) = 1…

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Q: Evaluate f(x, y, z) dS. f(x, y, z) = XY S: z = x2 + y2, 4 < x2 + y2 < 16

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Q: Find fxTy and f,, and evaluate each at the given point. (x, y, z) = x2y3 + 2xyz- 4yz, (-2, 1, 2) %3D…

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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: Evaluate [ f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

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Q: Let f(x,y,z)= x2y + xy2 + yz3 + xye2z Find fxz, fyz, and fzz

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Q: 14. Find the linearization, L(x,y,z) of the function f(x, y, z) = x³Vy? + z? at the pointP, (2,3,4).…

A: We have to find L(x,y,z) and by use of that we have to find the value of 1.9833.012+3.972

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: . Let u = [1, 7, 4]), v = [1,5, 5), and w [35, 25, 20]. Find the critical point of f(x, y) = (x · u…

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Q: Find f, fy, and f, and evaluate each at the given point. ху f(x, у, 2) 3D (6, 1, -1) x + y + z fa(x,…

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: Vy + z f(x, у, 2) 3 (а) f(1, 5, 4) (b) f(6, 7, –2)

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Q: •√ [F(x, Evaluate f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

A: We need to calculate ∬Sf(x, y, z) dS. Here,  f(x, y, z)=x2+y2+z2S=x+y, x2+y2≤1

Q: { 4, 0<x<y; 0<y<1; 0<x+y<1, f(x,y)= 0, %3D Otherwise. Calculate P(X <Y).

A: The provided joint density function is,

Q: Let f(x, y, z) = 6æ² + æy + yz + 7z?. Fina the linearization L(x, y, z) of f(x, Y, z) at the point…

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Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: z = f(st – 3, s+t°) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = fz(-1,9) = 2.…

A: (b) Apply the chain rule, ∂z∂t=∂f∂x×∂x∂t+∂f∂y×∂y∂tNow differentiate partially with respect to…

Q: In Exercises 61–64, find an equation for the level surface of the function through the given point.

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

Q: 9. Find fx and fy and f; for f(x,y,z) = (x² + y² + z²)~1/2 %3D

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Q: Find fy and f, and evaluate each at the given point. (x, y, 2) = x²y³ + 2xyz – 6yz, (-2, 1, 2) ,(X,…

A: Given :- f(x, y, z) = x2 y3 +2xyz-6yz  To find:- fx(x, y, z) fy(x, y,z)  fz (x, y, z)  fx(-2,1,2)…

Q: f., f, and f_, and evaluate each at the given point. x'y ху f(x, у, 2) 3- (4, 1, –1) x + y + z fx(X,…

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Q: Find f, fy, and f,, and evaluate each at the given point. z' fix, y, 2) %3D х*уз + 2хyz - 8yz, (-3,…

A: We will do partial differentiation.

Q: Evaluate F dr where F(x, y, z)= (x', y’, xyz) and C is the line segment from х, у, со (1, 4, 3).

A: Use parametric to solve

Q: A a,(x)y" +a-,(x)y"-|+...+a,(x)y'+a,(x)y=0 (x) y"-+ ...+a,(x)y'+a,(x)y=0 n-1 B a,(x)y" +…

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Q: (iv) If Z{y«} = Y (z), yo = 0 and y, = 1, then Z{y«+2} = z²Y – z. %3D (v) Z-1{ = 2* , k = 1,2,3, .

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Q: Find values of x and y such that  fx(x, y) = 0 and fy(x, y) = 0  simultaneously. f(x, y) = 7x3 − 6xy…

A: Given, f(x,y)= 7x³-6xy+y³ fx= 0 fy= 0

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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Q: 7. Compute , and- axay : f(x,y) = (x + y)(2x + y)² ax 'ay

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Q: Find fx and fy, and evaluate each at the given point. f(x, y) = arctan x/y , (4, −4) fx(x,…

A: Explanation of the answer is as follows

Q: Find F, and f, and evaluate each at the given point. fx, y, z) - xy + 2xyz - Syz, (-2, 1, 2) ,G Y.…

A: topic - partial differentiation

Q: Let f (x, y) = y³ + x² – 3y | Prove that the Critical points are (0,1), (0, – 1), (1,1), (–1,1),…

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Q: Suppose that w = f(x,y), x(s, t) = . = y(s, t) = And that fx(1,1) = 3, fy(1,1) = 4, fx(2,2) = 5,…

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Q: x = x(u, v), y = y(u, v), with x(-1,6) = 1 and y(-1,6) = 5, calculate z,(-1,6) in terms of some of…

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