Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz + 0. ду

Q: Given f(x, y) = x² – 3x?y – y", find fz(r, y) = fy(x, y) = frz(x, y) = fzy(x, y) =|

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Q: T(x,y, z) = x² + 2y² + z

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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 fx, fy and f z if f(x, y, z) = e*yz In zx. %3D

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Q: If x"y" = (x+y)* m, m+n d'y prove that = 0 .2 dx?

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

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Q: Determine dz for z = f(x, y) = e^(x^2+y^2) if x changes from 1 to 1.02 and y changes from 2 to 2.1.

A: use formula :-    dz = fx(x,y)dx + fy(x,y)dy

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If f(x,y,z) = e2x+3y-4z + xyz And x = 3si n(rt) y = 2cos(rt) z = r² + t² af Find at

A: Given that,  fx,y,z=e2x+3y-4z+xyz And  x=3sinrty=2cosrtz=r2+t2 If F=fx,y,z, Where, x, y, z are…

Q: Given f(x, y) = x° + 2xy³ – 2y", find fz(x, y) = fy(x, y) =

A: Given  f(x, y) = x6 + 2xy3 - 2y5.

Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: Given w = xysin(z²), x= s-t, y = s², z= t². Find ay

A: Explanation of the answer is as follows

Q: Given f(z, y, z) = V31 – 4y + 6z, find fz(x, y, 2) = fy(x, y, z) = f:(1, y, z) = %3D

A: Given :f(x,y,x)=3x-4y+6z

Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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Q: now if we take F (x, y) = (ax, ay), where a is any positive constan %3D

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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) 1* + 2xy° + 4y“, find fz(T, y) = fry(1, y) =

A: The given function is f(x,y)=-x3+2xy6+4y4

Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

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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: Given f(z, y) = 10/6z + 8y + 2xy®, find f.(T, y) = fy(z, y) = [

A: Given query is to find the indicated derivative.

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: J f(x)dx = f(x)dx =7, then J f(x)dx = If 4 and

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Q: Ifx' +y +z -2aņz =1, then show that V1-x dy 1- y V1-:

A: We have to use the given condition x2+y2+z2-2xyz=1 to find this.

Q: Find if f(x,y) = y sin xy ax %3D az Find ax if yz – In z 4. = x + y 3.

A: Given that: f(x,y)=y.sin(xy)   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: If f(x, y) = x²e + cosy af af then find dy

A: We will use partial derivative to solve this.

Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: Find ƒxx ( x, y)  and ƒxy( x, y).

A: Given, fx,y=3x+yx-1. The objective is to find fxxx,y and fxyx,y.   fxxx,y is found as follows: First…

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0)

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Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

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Q: If f(x, y, z) = xy + z?x - 3yx z?, find fxy ?

A: If fx,y,z=xy+z2x-3yx2z2 Find fxy ?

Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

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

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Q: x2 B) If w = x".f then show that: %3D x. Wx + y. Wy = nw.

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Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz 0. dx fie +

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Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

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Q: Given f(æ, y, z) = 6x² + 3y² + 4z², find f-(x, y, z) = | fy(x, y, 2) = | f:(x, y, z) =

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Q: Given f(z, y, z) = /1z2 + 3y? + 222, find %3D f-(z, y, 2) =| f,(z, y, 2) = f.(z, y, z) =

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Q: Let f(x, y) = x² + xy + y² where x = 3(t + s) and y = e2st, find . as

A: we have given f(x, y) where x and y are function of s and t.  We have to find the partial derivative…

Q: Given f(r, y) 2x* + 4x²y² – 5y°, find fz(x, y) - fy(x, y) = fzz(T, y) = fzy(T, y) =

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

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

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Q: Let y = f(x1, x2, w), where x1 = 2w2 and x2 = w+1. Find dy/dw.

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Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

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

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Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: Let f(x, y, z) = 3x?y+ yz3, where x = 3 – t2, y = 2t + t3, and z = V1+ 3t. Calculate when t = 1.

A: NOTE: Refresh your page if you can't see any equations. . here we have . the given function is…

Q: Find Duf at P. 2. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i+ 1 Duf = i

A: We need to find directional derivative at p.