Find f, and f, for f(x,y)=y In (3x +4y). fx fy

Q: 3. Find fz and fy where f(x,y) = In(x + y²).

A:

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

A:

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

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

Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

A:

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

A:

Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

A:

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

A:

Q: Find fr, fy, and fz. f(r, y, 2) — вуzIn(4ry) fz fy f: =

A:

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: Find fryz from the functions f (x, y, z) = 4x³y² – e²y+ ++ 4y – x16

A:

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: Find f, and fy. f(x, y) = 5x In xy %3D %3D fy =

A: Solution: The objective is to find the partial derivatives

Q: For the function f(x,y,z) = In (7x+ 2y +5z), find fy, fy, and f,. fx =口

A: Given,           fx,y,z=ln7x+2y+5z

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

A:

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

A:

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = xey.

A: Given function is fx,y=xey We have to verify fxy=fyx Solution: fxy means that first we find partial…

Q: Find ( fx fy, fzf xy f yx fxyz f zzx) for the function: f(x, y, z) = xyz + x²y + z³x + x²y?

A: To find the differentiation of the function

Q: If f(x, y) = 8xey + 8y Inx, then is given by:

A:

Q: .Determine if F(x, y) = (2xy + y-2)i + (x² – 2xy-3)j for y > 0 is conservative.

A:

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

A:

Q: If f(x, y) = 8xe2y + 8y Inx, then is given by:

A: The given function is: f(x,y)=8xe2y+8y ln x Now, ∂f∂x=∂∂x8xe2y+8y ln x       =8e2y+8yx

Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

A:

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

A:

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

A:

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

A:

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

A:

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

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

A:

Q: Find the particular sölution f"(x) = 4, f'(2) = 12, f(2) = 17

A: integration 2 times and after applying initial condition we get f(x)

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

A:

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

A:

Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

A:

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

A:

Q: If f(x,v) = (y)²x ,Verify fy=fx ху

A: Given:fx,y=y2x Now, the value of fxy will be,fxy=∂2f∂y∂x=∂∂y∂f∂x=∂∂y∂y2x∂x Now, the value of ∂y2x∂x…

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

A: It is partial derivative

Q: For the function f(x,y,z) = In (5x + 7y+ 9z), find fx, fy, and fz.

A:

Q: Given f(x, y) = x® + 3xy4 – 2y°, find f-(x, y) = fy(x, y) =

A: If f(x, y) is a function then, fx(x, y)  is differentiation of f with respect to x making y variable…

Q: Find all functions f(x, y, z) such that grad f = 2xi + zj + yk.

A:

Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

A:

Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

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

A:

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

A:

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

A:

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then:

A:

Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

A: