(a) By finding the marginal density fy(y), show that Y ~ Exp(1).

Q: dy sin x - y where f(n) = 0. dx %D |

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Q: Find the partial derivative of z with respect to u if: 2=x+4y, x= u sin v, y=u cos v

A: Partial differentiation

Q: Calculate the partial derivative of the function f(x, y, z) = xyz at the point (0, 1, 1).

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: Find the indicated partial derivative f(x,y,z) = x2cos(yz),     fxzy

A: Consider the function  fx,y,z=x2cosyz

Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

Q: Find the indicated partial derivative. f(r, y, :) = e"vz*; fzyz fxyz(x, Y, z) =

A: Given: f(x,y,z)=exyz3 To find: fxyz=?   Required formulas: Power rule: ddxxn=nxn-1 Product rule:…

Q: et f(x,y) be a function whose partial derivatives exist and are continuous at a point (a, b). Which…

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Q: Find partial derivative føyz of the function f(x, Y, z) = z ln x + 2y

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Q: 1. Show the range of (X,Y), Rxy, in the x – y plane. 2. Find the constant c. 3. Find the marginal…

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Q: Use the Chain Rule to evaluate the partial derivative at the point (u, v) = (0,5), where g(x, y) = x…

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Q: If f(x) = xe , x >0 and (Y = ln(X)), then the PDF of Y is %3D (In(1)² (In(y))e ye

A: Answer: ⊙ ey-12e2y

Q: Find the second partial derivative of the function f(z, y, z) = 2°yz+ at the point (1, 1, 1). yz

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Q: Compute the partial derivative of the function f(r, y, z) = e'-z cos(y) + z e=1/(1+y²) vith respect…

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Q: find a function z = ƒ(x, y) whose partial derivatives are as given, or explain why this is…

A: From both partial derivatives, we try to get a form for f(x,y). On the sin(xy) part we use by parts…

Q: Given the function f (x, y, z) = ln(x³ + 4y² – z) – x, calculate the partial derivative with respect…

A: Given function - f(x,y,z) = lnx3+4y2-z-xWhile differentiating f(x) with respect to x, then y and z…

Q: Let y = sin(5x). If Ax = 0.4 at x = 0, use linear approximation to estimate Ay Δy ~ Find the…

A: Given: y=sin(5x) ∆x=0.4  at x=0   Solution: y=sin(5x) For the function y=f(x),   ∆y=f(x+∆x)-f(x)…

Q: 3. Find the partial derivatives du and ou if uw = x sin (y), x = s² +t? and y =;,

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Q: ӘТ ӘР V

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Q: Find the indicated partial derivative of the function f(x, y) = sin(2x + 5y). Answer: fyæy(x, y) =|…

A: Solve the following

Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: to Find the first partial derivatives of g(x,z) = x In (z dg dx ag dz

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Q: -u = x"y' z°; dx dy? Əz³

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Q: Compute the indicated partial derivative. 5x g(x, y) = x + 2y a?g ду? =

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Q: Find the partial elasticities of z = x'e.

A: Introduction: The partial elasticity of z with respect to x is given by, εx=zxxz The partial…

Q: Find the first partial derivatives with respect to x, y, and z.…

A: w=7xzx+y Partially differentiating with respect to x, we get ∂w∂x=∂7xz∂x·x+y-∂x+y∂x·7xzx+y2…

Q: Compute the partial derivative: f(x, y) = sin(x" –- 3y) fy(0, ) =

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Q: Xyz f(x.y.z) = function is given dt P(2,t,) in point fax + fy + f2z colculate.

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Q: Find the Partial derivative of f with respect to y for * 2. y² f (x, y) = x + y

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Q: Compute the partial derivative of the function f(x, y, z) = e'-z cos(y) +ze-/(1+y²) with respect to…

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Q: Given the function f (x, y, z) = ln(x³ + 4y² – z) – , calculate the partial derivative with respect…

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Q: fxx (x, y) = (x + y²), 0sx<1,0<ys1 a) What is the marginal pdf of fy (y)? b) What is the conditional…

A: Solution: From the given information,

Q: For an ideal gas, find explicit expression for the partial derivative:* ƏT RT P R. O Option 1 O…

A: The equation of an Ideal gas is PV=nRT. Here, P- Pressure V- Volume n- Amount of substance R- Ideal…

Q: Find the marginal PDFS fx (x) and fy(y).

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Q: Given that e2y, 10x2+4. f (x, y) = sin Enter a 10 significant figure approximation to the partial…

A: We will use matlab to find the answer

Q: Find the total differential z = e−x tan y

A: we have to find the total differential of z = e−x tan y           dz=∂f∂xdx+∂f∂ydy        (1) where…

Q: If f(x, y) = e"sin (x), evaluate the partial derivative f, at (, 0). A. π В. 1 C. 0 D. - 1 E. None…

A: First we find out fx then we put x=π and y=0 in the value of fx .

Q: Find the indicated partial derivative. f(x, y) = y sin-1(xy); (2, #) /2. 4) L

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Q: Find the orthogonal trajectories of y = e where a be the arbitrary constant.

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Q: fxx (x,y) =(x + y²), 0<xS 1,0 <ys1 a) What is the marginal pdf of fy (y)? b) What is the conditional…

A: Solution: The given joint pdf of X and Y is

Q: Compute the partial derivative: f(x, y) = sin (a- 6y) f,(0, T) =

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Q: Find the first partial derivatives with respect to x, y, and z. 3xz w = x + y aw ax aw ду dw az

A: To find the partial derivatives of the function

Q: Let y sin(5x). If Ar 0.3 at z 0, use linear approximation to estimate Ay %3D Ay = = Find the…

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Q: (b) Find the partial derivative at point (u,v) = (-4,0) of w = In(xª + yß + zª),x = ue"sinu, y =…

A: Chain rule:  Suppose that  are differentiable functions of and  is a differentiable function of .…