Use chain rule and compute dx/dv if z=x2+xy3, x=uv2+x,w3, y=u+vew

Q: X, X2 ixd.u Co1) yi= Xi+X2 ェニメルナメ」 %3D d distribution

A: first consider the joint density!!

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 4xyz + 7yz2 s(x,…

A: As we know that the sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 Given:…

Q: Find all the second partial derivatives. f(x, y) = x^y – 3xSy2 fxx(x, y) fyr(x, Y) %3D

A: Given: f(x,y)=x4y-3x5y2

Q: 3.2= e'-ry ; I=t3 and y = t° %3D

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Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = √u and u = x3

A: Recall the chain rule of differentiation:

Q: Compute the partial derivatives: = Z +y? || ||

A: Partial derivatve is

Q: Find the first partial derivatives with respect to x, y, and z. 3xz w = x + y aw Əx aw ду aw %3D Əz…

A: Here we need to find the partial derivatives of the given function with respect to x, y and z. While…

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: Find the first partial derivatives of (a) f(x,y,z)=x²yz³ (c) S(x,y,z)= In(#)+ tan""(yz) (b)…

A: Solution of first partial derivatives.

Q: Find the first partial derivatives of the function. 4x – 7y f(x, y) = %3D 4x + 7y A(x, y) = Wx, y) =

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

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Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: Show that B is a linear function of Y,, Y2. Yn Show that B is conditionally unbiased.

A: The regression model is  Yi = βXi + ui We have to show that β is conditionally unbiased.

Q: Find the first partial derivatives. (x, y) = xFye-5y ,(X, Y) = ,(x, V) =

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Q: Use the Chain Rule to find the indicated partial derivatives. z = x3 + xy4,    x = uv3 + w4,    y =…

A: According to the given information, it is given that:

Q: Find both first partial derivatives. z = exy az ax dz II

A: topic - partial derivatives

Q: Find the approximate solution of the Poisson equation uxx + Uvy = -1, x| < 1, ly| < 1 u = 0 at x =…

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Q: Use the Chain Rule to find the indicated partial derivatives. R = In(u2 + v2 + w?), u = x + 6y, v =…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4xy – 9xyz + 8yz² fx(x,…

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Q: Find the first partial derivatives of at the point (x, y) (1,2). x + y f(x, y) af -(1,2) = 2/3 af…

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

Q: Find all the second partial derivatives. u = x²y^z6 Uxx(x, y) = Uxy(x, y) = Uyx(x, y) = Uyy(x, y) =…

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

Q: Compute the indicated partial derivative. g(x, y, z) = x³y^z° 9xxyz =

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Q: Find the first partial derivatives of the function f(x, y, z) = xz – 5x²y³z*.

A: Find the first partial derivative of function f(x,y,z)

Q: Find all the second partial derivatives. x, V) = x^y% + 2x5y x, v) = II

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Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = u3 and u = √x

A: Given: ,and . Find out by using the chain rule.

Q: Use chain rule to find given x² + 2y² + z² and x os (st), y %3D Cos

A: Solve the following

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: Use the Chain Rule to find the indicated partial derivative z = x3 + xy4, x = uv + w3, y = u + vew…

A: we have been given the equations such as z=x3+xy4, x=uv4+w3, y=u+vew…

Q: Find both first partial derivatives. Z = 13xVy az %3D az %3D ay

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Q: Find both first partial derivatives. f(x, y) fx(x, y) = fy(x, y) = ху ,2 x + ,2

A: Find the partial derivatives

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x2y – 3xyz + 7yz?…

A: Partial derivatives

Q: 2. Find the matrix of chain rule given u = xy + xz + yz; x = cos t, y = sin t, z = t.

A: Given

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y – 9xyz + 8yz2 syz?…

A: The objective is to find partial derivatives with respect to x, y and z.

Q: Use chain rule to find the partial derivatives and given z =x²y+sin (x+ y), u+v x = u+ uv, y = e"*,…

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Q: How many second partial derivatives does ƒ (x, y, z, t) have?

A: We have to find the number of second partial derivatives.

Q: Find all the first partial derivatives of z = 5x°y - 8xy*. (Choose all applicable answers.) O zz =…

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Q: Find all the second partial derivatives. f(x, y) = xªy – 2x³y² fxx(x, y) = fxy(x, y) = fyx(x, y) =…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: Compute the matrix of partial derivatives of the following function. f(x, y, z) = (x + z, y - 5z, x…

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Q: Suppose that u = x²y, where x = r cos 0 and y = r sin 0. du Compute the partial derivatives du and…

A: Given that u=x2y  ….(1) where x=rcosθ  and y=rsinθ Differentiating (1) partially with respect to 'r'…

Q: Compute the partial derivatives. z = x5 - y6 əz 1 5x - ,6 dz ду II II

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Q: Compute the partial derivatives: = In(x" + y*) dz dz dy ||

A: handwriting solution

Q: If z = sin(x/y) and x = ln (u) and y = v^4, find the partial derivatives of z with respect to u and…

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Q: Compute the partial derivatives. 6x z = V x2 + y2 az 2 V 2x +y dz ду

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Q: Find the first partial derivatives with respect to x, y, and z. 7xz W = x + y aw ax aw ду aw az ||

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Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

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Q: Find the first partial derivatives of the function. f(x, у) : cos(t5) dt fx(x, y) = fy(x, y) =

A: We use the leibniz derivative.