Given w = f(x, Y, z) =

Q: Given f(z, y) = – 3z' + ry° + 5y², find fr(x, y) = | fy(z, y) = |

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Q: Show that: H(X,Y) = %3D H(XY) + H(Y)

A: We have to show that H(X,Y)=H(X/Y)+H(Y)

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: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

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: (a) f(x,y) = (x² + 1)e" (b) g(w, z) = w? + 22 (c) h(x, y, z) = vT² + 3y – xyz²

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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: 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: Given: z = x3 + xy", æ = uv + w°, y = u + ve" az when u = 3, v = – 2, w = 0 Find

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Q: Calculate fff(x, y, z) dS For s f(x, y, z) ds x² + y² = 16, 0≤ z < 2; f(x, y, z)=e*

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Q: Given f(r, y) = yln(5z+ y), find .(e, v) - 1,(2, u) = %3D

A: We have to find derivative

Q: Find ∂w/∂r for w = yz/x, x = θ2, y = r+θ, z= r-

A: To evaluate ∂w∂r

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: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

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Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

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Q: If f(x, y) = xy then: V f(1, – 1) =

A: Given function is,  f(x,y)= xy

Q: Given w = f(z) = (1+z)/(1 – z), find (a) dw/dz

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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: If f(x, y) = (xy)", with |xy| < 1, find 2 af af and n=0 fe -y/(1-xy)^2 af -x/(1-xy)^2 dy

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Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

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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: Evaluate S, y dv with E = {(x, y,z): 0 <x< 3, 0< y < x, (x – y) < z < (x + y)} %3D

A: Use triple integration

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: 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: Evaluate 3xz dV where E {(x, y, z) | 2 < x < 5, x < y < 2æ, 0 < z < x + 2y}

A: Given,

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: Calculate s f(x, y, z) dS For y = 2 – 22, f(r, y, z) = ls f(x, y, z) dS

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Q: Calculate ∬S f(x,y,z) dS For y=2−z^2,   0≤x, z≤7;    f(x,y,z)=z

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Q: Evaluate 3xz dV where E = {(r, y, z) | 2 < ¤ < 4, x < y < 2x, 0 < z < x + 2y}

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

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Q: Let f (x,y) = e**ytan (x + y), find дудх

A: Explanation of the solution is given below...

Q: If F = x?z + e (y/x) and G = 2z?y-xy?, find: 1. V(F+G) 2. V(FG) at point (1,0,-2)

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Q: Given f(æ, y) = e"" Y' – z°y", show that fæy = fyæ.

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Q: (x + 2y), 0sx<1,0<y<1 fx: 0, elsewhere PG<x<를 &y<b a.

A: Given,f(x)=23(x+2y); 0≤x≤1 , 0≤y≤10; elsewhere

Q: Given f(x, y) = 3x° cos (y"), find f-(r, y) = fy(x, y) = fae (x, y) = fyz (x, y) =

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Q: Given f(x, y) = – 5x + 6xy° + 3y, find - fa(z, y) = %3D f,(z, y) = !!

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Q: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

Q: f(x, y) = e&z– 4y af af ду

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

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Q: Find vf(x, y) if f(x,y) = e* c cos y 5.

A: Note : according to our guidelines we can answer only first question because there are multiple…

Q: R = {(x,y) E R ×x R : x > y} T = {(x, y) E R × R : x > y}. RoT.

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Q: O A. E(YZ) – E(Y)E(Z) OB. E(Y|Z=z)=[* O B. „yf(y|z)dz OC. F(y.z)=F(y)F(z) OD. V(Y|Z=z)=E(Y²)-(E(Y))²

A: Correct answer is B. E(Y|Z=z) = ∫-∞∞ yf(y|z) dz

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

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Q: Given f(x, y, z) = 4x2 + 2y? + 6z?, find %3D fa(x, y, z) = fy(x, y, z) = f:(x, y, z) =

A: To find fx(x,  y,  z) =........... fy(x,  y,  z) = ...........  fz(x,  y,  z) =............

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(z, y) – zsiny +e, then Vf(r, y) (0, e").

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Q: Find (∂ w/∂ x)y, z if w = x2 + y - z + sin t and x + y = t.

A: To find the partial derivatives.

Q: f (x, y, z) = xªe²y+æ² zy? – 5zæy³ | af af af dx ' dy' dz Determine

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Q: Find Vf(x, y) if f(x,y) = e** cos y ..... ...

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