Suppose z x'y' where x-st and y -t -s. Use the chain rule to determine as and a) -2xy't-4yx's;- 2xy's-4yx't at b) - 2xy's- 4yx't; 2xy't-4yx's %3D -2xyt - 4yx's: - 2xys-4yx't d) - : -2xy's-4yx't 2xy't-4yx's as 一 さ8 22だ13

Q: Consider the functions z = -8 ex In y, x= In (u cos v), and y =u sin v. dz as a function of u and v…

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Q: (c) Compute of using the Chain Rule. of дf дх дf ду дf dz. + дя дх дя ду дя дz дя (Use symbolic…

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Q: 2. If T = u? + v²,u = x+ y+z,v= ryz. Using the chain rule to find and when r = 1, y = 2, z = 3. Draw…

A: Given that: T=u2+v2u=x+y+zv=xyzx=1, y=2, z=3

Q: Use Chain Rule to find given w = ds x2 – 2y + z2 and a = cos (st), y = -2s In t and z = s – - VE.

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Q: 6. Use the Chain rule to determine fs, an f(x, Y, z) =

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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: az az Use the chain rule to find and as at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az %3D…

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Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: 1. Use the Chain Rule to find dy in terms of r. dr а у — (и—2)3 and и- 2x +1 b. y = Jū and u= 5z2 –…

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Q: Find both first partial derivatives. Z = In az %3D ax az ду

A: ∂z/∂x = 1/x    ∂z/∂y= -1/y

Q: Differentiate ysin(1/y)=1-xy

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Q: az az Use the chain rule to find and as at Z = In(3x + 5y), x = s sin(t), y = t cos(s) az az at

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Q: compute the first-order partial derivatives. z = 9 − x2 − y2

A: z=9-x2-y2

Q: dw Use the Chain Rule to find dt w = 7x°y°z,x = 2t, y = cos(4t), z = tsint %3D 7xy°(12yz -…

A: see 2nd and 3rd step.aa

Q: ) If ƒ(x,y) = 3x²y + cosy+ ysinx – e2x then verify fxy = fyx

A: fx and fy are the partial deferential of function w.r.t x and y respectively. Then fxy is the…

Q: could I get help finding all the 2nd order derivatives please

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Q: Find all second-order partial derivatives for the following. 4.6 5,7 R(x,y) = 5x* - 2x*y+6x°y7 2,6…

A: R(x,y) = 5x4-2x4y6+6x5y7Ry = 0 - 2×6×x4y5 + 6×7x5y6Ry = -12x4y5 + 42x5y6

Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

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

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Q: 2. Show that the Euler-Cauchy Equation Iy" + axy + by = 0, 1+0 can be transformed into the constant…

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Q: 비 az and Given that z = e*, x= 2u+ v, y= .y==. Find using the chain rule. au

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Q: Use the chain-rule and find x and y in terms of x, x, and if:

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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 the Chain Rule to find az/əs and ôz/Ət. z = tan(u/v), u = 8s + 3t, V = 3s – 8t

A: z=tanuv,   u=8s+3t,   v=3s−8tFormula→∂z∂t=∂z∂u⋅∂u∂t+∂z∂v⋅∂v∂t

Q: let z- 57 dy .. dy By chain Ruie

A: The objective is to find the second derivative using chain rule.

Q: Let ƒ (x, y) = x³ − x² − 8x + 2xy − - - 12y². (a) Compute all first order and second order partial…

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

A: Solve the following

Q: Find both first partial derivatives. z = cos(10xy) az ax az ||

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Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.

Q: Let f(x, y, z) = 4xy – z², x = 6r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

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Q: Compute the partial derivatives: ,2 z = In(x² + y³) az dy

A: Use partial derivative

Q: 2] write the chain rule formula for the derivatives Of and E , where Z=ZCrisit).

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Q: chain

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Q: Suppose that z = z(r, s,t), where r = u+2v, s = 3u and t 4v. az Compute the partial derivatives and…

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Q: exercise 1 Find all fist and second partial derivatives of the following: (a) z= 4x³ – 5xy² + 3y³…

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Q: Q2-By using Chain Rule, find au/ax, du/dy, du/dz at (x, y, z) = (√√3,2,1) U= p-q q-r p=x+y+z…

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Q: Suppose that w = f(x,y, z), x = h(s), y= g(s, t), z= k(s,t) and all the conditions required for the…

A: Given that w=fx,y,z, x=hs, y=gs,t and z=ks,t. We have to compute ∂w∂t by using chain rule. Since, by…

Q: az Use the Chain Rule to find at for z = In(x? + y), x = st, y = t/s.

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

Q: Let z = √7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2.

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Q: 9. Find all the second partial derivatives of Z; given: a) Z = xy³In(3xe' )

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: Verify the chain rule y = t³. %3D

A: Given query is to solve the expression using chain rule of derivative.

Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

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Q: 4y" – y = 0, У-2) %3D 1, у(-2) %3D -1

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Q: Let z = f(x, y) and suppose x = 2u – 3v and y = 5u + 6v. Use the chain rule to express dz in terms…

A: x=2u-3vy=5u+6v Now we apply the chain rule  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u Take derivative of x  and y…

Q: Let z = F(x , y) = xy2 + - , where x = u2 + v2 - 4 and y = uv . az Use the chain rule to find at (u…

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Q: Verify the chain rule for jacobian, if y2 u = x + , v = * y2 %3D

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