Let X and Y have the joint pdf f(x, y) = (1 – xy), 0 < x < 1, 0 < y < 1. Find E(X).

Q: Find the total differential. z = e-X tan(y)

A: Given, fx=z=e-xtany To find fx=z

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Find the derivative of the function h (x, y, z) = cos xy+ e+ In zx %3D at P. (1, 0, 1/2), in the…

A: Here we have to find directional derivative of h(x,y,z) in the direction of u.

Q: dz Use the Chain Rule to find dt for z = x2 + y2 + xy,x = sin t , y = e'.

A: z=x2+y2+xy ; x=sint , y=et

Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: A joint pdf of X and Y is given by f (x, y) = xy² for 0<x<2,0< y<2. 16 3 a) Find P(X<1,Y <1) .

A: Given that, f(x,y)=316xy2, 0&lt;x&lt;2, 0&lt;y&lt;2 a) PX&lt;1, Y&lt;1=∫01∫01f(x,y)dxdy…

Q: The joint PDF of X and Y is given as S2, 0< x< y<1 f(x,y) (0, otherwise

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Q: The joint PDF of X and Y is given as 0<x<y<1 (2, f(x, y) = Q. otherwise

A: Given: f(x,y)=20≤x≤y≤10otherwise

Q: 4. Use the chain rule to find out the total derivative dv/dt, when v = xe/z, where r = t²,y = cos t,…

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Q: Determine the total differential (dg), and total derivative with respect to x 3x 2y g f(x, y, z) 3D…

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Q: Let y = tan find the differential dy of the function.

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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 value of the derivative of ƒ(x, y, z) = xy + yz + xz with respect to t on the curve x = cos…

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Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Suppose that X and Y have joint pdf (8xy 0< y<x<1 f(x, y)=- otherwise Find the joint CDF. Find fy…

A: Given:

Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: x2y2=2y3+1

Q: The distributional second derivative of u(x) = |x|, Vx R is given by O бо 0-80 O 0. 200

A: To find the distributional second derivative of ux=x, ∀x∈R.

Q: Given Lve f(t) dt = In(x) cos(x) + sin(3) :L.e- f(t) dt, find f(x). sin(3)

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Q: Use the appropriate multivariable chain rule to find the indicated derivative. a. Let w = f(x,y,z) =…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Assume that X and Y have joint pdf Sr + 3x?y if 0 <r<1 and 0 < y < 1, f(x, y) = %3! otherwise.

A: We know that, Covariance(X,Y) = E(X).E(Y) - E(XY) Here E(X) and E(Y) are given so we'll Calculate…

Q: Let y be a function of x . If y“ = tan(x² +y² ) + e®, find dy by implicit differentiation. dx

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Q: The joint PDF of X and Y is fær(x, y) = {"e * 0sy<x] otherwise .

A: The joint PDF for X and Y is, fx,y=λ2e-λx, 0≤y&lt;x   Given that W=X-Y Let Y=V W+V=X Consider, the…

Q: 1. Find the total derivative dz/dy, given (a) z= f(x, y) = 5x + xy – y², where x = 9(y) = 3 y2 (b)…

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Q: Let y= tanx .(a) Find the differential dy .(b) Evaluate  dy and ∆y if x= and π /4 and dx =-0.1.

A: Given function is (a) Differentiating with respect to x, we get

Q: Find the total derivative of the function f(x, y, z) =+z In (2x+1)+sin (xy) xz

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: Determine the total differential (dg), and total derivative with respect to x 3x 2y f(x, y, z) =…

A:

Q: Let y = tan x. (a) Find the differential dy. (b) Evaluate dy and Δy if x = π/3 and dx = -0.2…

A: Let,  y=fanxa To find differential dy, differentiate y       with respect to x,        dy=sec2x dx

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: Given, y = cos2x We have to find dy/dt when x=π/4, given dx/dt=−4 when x=π/4.

Q: The joint PDF of the r.v. A and B is constant on (a, b): a, b > 0n 0.5 0.5|X<0.5).

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Q: Suppose that x and y are both differentiable functions of t and are related by the given equation.…

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Q: b) Find the value of the derivative of f(x, y, z) = xy + yz + xz with respect to t on the curve x =…

A: There are two methods to do this: One is direct method which we used and other is by chain rule.

Q: Let X, Y have the joint pdf {; for x? + y? 0, y > 0 cx fx,y O.W. where c is some constant.

A: Given that,

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: partial differentiation

Q: Let X have the pdf 1 p(x) = T(1+ a2)' x E R. %3D Find the pdf of Y = X?.

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Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: Evaluate dt dW at t=0 for the function W = e' – In x , x = t², y= In t

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Q: Find the derivative of the function at Po in the direction of A. g(x, y, z) = 3e* cos yz, Po(0, 0,…

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Q: The joint pdf of two variables X,Y is fxy(x,y)=ae **9) for x20, y20. Find the constant a. Are X and…

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Q: Find the derivative of function ei, x#0 1 еx, f (x) = 0. at xo = 0 X = 0

A: Find the derivative of the given function.   Given: fx=e1x, x≠00, x=0

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: Find the derivative of y with respect to x. y = tan -1V3x O A. V1- 3x 1 O B. 2(1 + 3x)/3x 3 Oc.…

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Q: implicitly dx

A: Solved below

Q: Given the joint pdf of X and Y is fxy(x, y) Find P(X>Y). = -{abe abe-(ax+by) x>0, y>0 otherwise

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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