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

Q: Compute the values of dy and Ay for the function y= e4z + 5z given z = 0 and Az = dz = 0.02.

A: Given x = 0, dx = ∆x = 0.02            (1) Here y = f(x) = e4x+5x

Q: Given f(x, y, z) = 3x – 2y + 1z, find f. (æ, y, z) = fy(x, y, z) = f:(x, y, z) = |

A: We are given with the function f(x,y,z) and need to find the derivative fx,fy and fz.

Q: Find f, and f, and evaluate each at the given point. 4xy f(x, у) %3D (1, 1) V 2x2 + 7y2' f,(x, y) =…

A: This question is related to partial derivatives as solved in step 2.

Q: 1. Find V · (V × F), for F(x,y, z) yzi + xzj + xyk.

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: 3. Find V x F for F(x, y, z) = -IZ i+ x² + y² -yz 1² + y² +√x² + y²k.

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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: Find ∂ w/∂ x at the point (x, y, z) = (2, -1, 1) if w = x2 + y2 + z2, z3 - xy + yz + y3 = 1, and x…

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Q: if f(x,y)= ln(x^2 +y^2), find fxx(x,y) + fyy(x,y)

A:

Q: Q1. If g = xy - yz - · — zx and F = x²y ī − 2 y²zī – z²x k, find F. grad g and cross product of F…

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

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Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=< 3x2y-z, xz3+y4, -2x3z2 > To Find , grad divV  Let  V=< V1 ,V2 ,V3 > On…

Q: Find the maximum and minimum vvalues of f(x,y)=x3+3xy2-3x2-3y2+4

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Q: Given f(x, y, z) = 2e(z+y), Find fy(0,},-4).

A: here we have to find partial derivative of a function w.r.t. 'y' and here we also use chain rule.

Q: If Z = x.n. f .f (**²), then show that: X. Zx + y.Zy = y

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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: o Find the Vf at the given point 1.f (x,y,2)=x² + y² -2:2 +z In x,P(1,1,1)

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Q: Find f, and fy, and evaluate each at the given point. 7xy f(x, y) (1, 1) V4x² + 5y² fx(x, y) = f,(x,…

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Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

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Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: f (z,y, z) = x² + y² + 2² subject to zyz = 4

A: Given: fx,y,z=x2+y2+z2 subject to xyz=4 Let gx,y,z=xyz-4 Using Lagrange Multiplier fx=λgx, fy=λgy,…

Q: Find f, and f and evaluate each at the given point. 2xy x, - V+ ay (1, 1) K, ) - Sx, ) - (1, 1) - 29…

A: The solution of the problem is given in the next steps.

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

A:

Q: 6. Let z = f(x, y), find and of (a) xy – yz + xz = 0 (b) xz² + 2x²y= 4y²z-3y+2

A: Here z is function of x and y . So to find partial derivatives of z w.r.t. x and y we have to apply…

Q: Find values of x and y such that both f,(x,y)= 0 and fy (x.y)=D0. f(x.y) =x + xy +y² - 3x+2

A: Given that, the function is fx,y=x2+xy+y2-3x+2. Obtain the value of fxx,y.…

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

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Q: 2. Let f(x,y)=xe" and find a) fx, fyr fy

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Q: £f*. S: z = 18, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

A:

Q: Find and given f(x, y) = y" In(x²) + - Va 8y

A: Given: Function in x, y is given.          fx,y=y7lnx2+9y3-x47 Objective is to find,…

Q: Find fy, fy, and f, for f(x,y,z) = 4xy + 6xz + 2yz.

A: Given, f(x,y,z)=4xy+6xz+2yz

Q: Q1. If g = xy — yz — zx and F = x²y ī − 2 y²zī – z²x k, find F. grad g and cross product of F and…

A:

Q: Evaluate [lR fx, Y, z) dV for the specified function f and B: f(x, y, z) = 3 <a < 6,0 < y < 2,0 < z…

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Q: Q3: 1f f(x, y) = 4xCy5 + 6x*y* .Prove that: f(x,y) * fxxyy fxx * fyy = 1

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Q: Q3. If F = x'a, + y'a, + (z² – 1) a̟, find F· dS, where S is defined by r= 2, 0 < z < 2,0 < ¢ < 2r.

A:

Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: Find f, and fy, and evaluate each at the given point. 2xy f(x, y) = (1, 1) V 2x2 + 2y2" f,(x, y) =…

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Q: Find fy and f, for f(x, y) = 10(4x – 5y + 11)°. f, (x.y) =O fy(x.y) =|

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Q: 3) f(x, y, z) Зху %3D z- Vx

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Q: Find f,, fy, and f, for f(x,y,z)= 5xy+ 3xz + yz.

A: It is partial derivative

Q: 8. xyzx +2y³ (z, = 1

A:

Q: If F (x, y, z) = e^xz i + 3xe^y j − e^yz k, then find ∇.(∇ × F)

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Q: Q1/ find Vf at the given point. 1. f(x, y, z) = x² + y² – 2z² + z In x, (1, 1, 1) 2. f(x, y, z) =…

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Q: Find fx and fy, and evaluate each at the given point f(x, y) = exy2,   (ln 3, 2)

A: Given:  f(x, y)=ex y2 ;    (ln 3,  2)To…

Q: Find the values of ∂z/∂x and ∂z/∂y at the points z3 - xy + yz + y3 - 2 = 0, (1, 1, 1)

A: Given: z3-xy+yz+y3-2=0  At the points (1,1,1) To find: The values  of ∂z∂x and ∂z∂y.

Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

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Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

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

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Q: Find f, and fy, and evaluate each at the given point. 'y' f(x, y) = arctan(), (2, -2) f(x, y) =…

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Q: 2. f(x, y, z) = exyz² Find fxyz

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

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Q: Given the function: f(x, y, z) = x²yz + xy+ +1 find: fz(1, 2, 3)

A: We will find fx1,2,3 in the following step.