Consider the functions f(x, y, z, t) z?, t?) and g(u, v) = (uv, u +v, u – v). Use the chain rule to (x2 + y? + compute D(g o f).

Q: Let w = f(r.0) where r and 0 are functions of s and t, then according to the chain rule is equal to…

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Q: dz Q\ let z = 8x'y-2x +3y, x = uv, y = u + v use the chain rule to find du

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Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: dw dw and du For the functions w =xy + yz + xz, x=u + v, y =u - v, and z= uv, express using the…

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Q: Let f (x, y) = (x − y)e^x . Use the Chain Rule to calculate ∂f/∂u and ∂f/∂v (in terms of u and v),…

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Q: Use the Chain Rule to find dw/dt. w = xey/z,    x = t5,    y = 1 − t,    z = 3 + 7t

A: To find out dw/dt.

Q: Let f(x, y, z) = x²y³ + zª and x = s², y = st², and z = (a) Calculate the primary derivatives - af…

A: fx, y, z=x2y3+z4  &  x=s2, y=st2,  &  z=s2t a). ∂f∂x=∂∂xx2y3+z4=y3·2x+0=2xy3…

Q: use the Chain Rule to calculate f (r(t)). 8(x, y, z, w) = x + 2y + 3z + 5w, r(1) = (12, 13, 1, 1–2).…

A: Given, g(x,y,z,w)=x+2y+3xz+5w, r(t)=t2,t3,t,t-2, t=1 To find ddtg(r(t)).

Q: tu+v dt In(t) f(u, v) = u-1 fy Find using the chain rule u = x +y³, v= 3y- 3xs

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Q: Use the Chain Rule to find ôz/ðs and ôz/ôt. z = tan(u/v), u = 9s + 8t, v = 8s – 9t as az at

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Q: Find the linearization L(x,y,z) of the function f(x,y.z) at the given points. f(x.y.z) = e* + cos (y…

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Q: Solve the following function by applying the chain rule. w = xyz x = u?v y = uv? Z = u? + v? %3D…

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Q: Use the generalized chain rule Question of Let f(x, y, z) = 2x(y+ z), x = uv, y = v + w, and z = w².…

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Q: Use the Chain Rule to find dw/dt. w = xey/z,    x = t5,    y = 3 − t,    z = 1 + 2t

A: Please find the detailed solution in below image

Q: Use the Chain Rule to calculate f(c(t)). dt f(x, y, z) = xºy®e4z, c(t) = (t², t³, t – 1), t = 1…

A: To Determine: Use the chain rule to calculate:                                       When…

Q: If z = f(u) + g(u), where u = = and v = x · y. Prove that x · Zx – y · Zy = y² ·Zyy – x².Zxx using…

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Q: Use the Chain Rule to find əz/əs and əz/ət. z = (x - y)5, x = s?t, y = st2 az as az at

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Q: Use the Chain Rule to find dz/ðs and əz/ət. z = tan(u/v), u = 5s + 8t, v = 8s – 5t %3D az %3D as az…

A: We have to use chain rule to find the partial derivatives of z.

Q: Use the Chain Rule to find- af when r = 2, t =-1 of the function ar f(x, y, z) = e3xyz cos 2xyz ; x…

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Q: Let f(x,y)=xy^2 and r(t)=⟨(1/2)t^2,t^3⟩. Use the Chain Rule for Paths to evaluate d/dtf(r(t)) at…

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Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: (a)

Q: | Let u = x*y + y°23 where x = rse', y = rs²e=t, = 2, 8 = 1 and t = 0, by using Chain Rule. p2 Sint.…

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Q: Use the Chain Rule to calculate dt (r(e)). f(x, y) = 3x – 2y, r(t) = (t°, t°), t = 2 (2, 8), t = 2

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Q: se the chain rule to compute and at (u, v) = (1, I) where f(x, y, z) = x²y + y²z + z²x and r(u, v) =…

A: Given: fx,y,z=x2y+y2z+z2xr→u,v=eucosv,eusinv,u2u,v=1,π4 To find: ∂f∘r→∂u=?∂f∘r→∂v=? Concept used:…

Q: Consider the functions f(x, y, z, t) = (x² + 2. t²) and g(u. v) = (uy, u +v. u – v). Use the chain r

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Q: Use the Chain Rule to find ðz/ðs and az/ðt. Z = tan(u/v), u = 8s + 9t, V = 9s – 8t %3D az ds az at

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Q: For the functions w =xy + yz + xz, x = 3u + v, y= 3u - v, and z = uv, express , and , using the…

A: Here, w=xy+yz+xzx=3u+vy=3u-vz=uv

Q: Find the domain of the piecewise function: x < 0 0<x <1 2х, y = In x, Vx-1, x 21 Select one: O a. x…

A: By finding the domain of each piece definition of functions we thereafter take the union of all to…

Q: Use the Chain Rule to find dw/dt. w = xey/z,    x = t7,    y = 1 − t,    z = 3 + 7t

A: We use the product rule then chain and quotient rule

Q: Use the functions below to ​(a) express ∂z∂u and ∂z∂v as functions of u and v both by using the…

A: From the chain rule, ∂z∂v=∂z∂x×∂x∂v+∂z∂y×∂y∂v…

Q: Let z = f(x, y) = e**y while x = 2st and y = s² + t³. Use a chain rule to find ôz/8t at the points…

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Q: Use the Chain Rule to find az/as and əz/ət. Z = tan(u/v), u = 7s + 5t, V = 5s – 7t az ds az at

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Q: Use the chain rule to find D (f o g) (–1,2) for f(u, v, w) = (v² + w², u³ – vw, u²v+ w) and g(x, y)…

A: This question is related to derivative of composite function.

Q: Find the divergence of F. F(x, y, z) = 8xi + 8y²j + 8z²k

A: Given,           Fx,y,z=8x2i+8y2j+8z2k

Q: Find z'(t), where z = In (x + y), x = 2t e', and y = 5e', in the following ways. a. Replace x and y…

A: follow next step

Q: Use the Chain Rule to find zz and zy given sin(u) tan(v), u = 3x + y, and v = x – y. %3D

A: Given z = sin(u) tan(v)where u = 3x + yv = x - y

Q: Use the chain rule and compute if z = x2 + xy, x = uv? + w°y = u + ve"

A: z=x2+xy3, x=uv2+w3, y=u+vew

Q: 41. Let f(x, y, z) =x?y+ y²z. Use the Chain Rule to calculate af/as and af/at (in terms of s and f),…

A: Since f is function of x, y and z.  For partial derivative f with respect to s and t we using chain…

Q: Express dw/dr and dw/as as functions of r and s using chain rule w = In(x + y + z*), x = re sin r, y…

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Q: c) Use the Chain Rule to compute %3D ds se In (c) express your answer in terms of the independent…

A: Here, the given functions are: f(x,y,z)=x4y+z4, x=st2, y=st,z=s2t

Q: d(f o r) Use the chain rule to compute where f(x, y) = x² + y² and ř(t) = (t2, t) dt d(f or) dt

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Q: Given w = f(x, y, z), x = g1(r, s), y = g2(r, s), and z = 93(r, s), write the chain rule for ow and…

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Q: Find ∂w/ ∂r and ∂w/∂t (a) by using the appropriate Chain Rule and (b) by converting w to a function…

A: Given: w=xyz  ;   x=2r+t,  y=rt,…

Q: Use the Chain Rule to find ôz/ds and ôz/ðt. z = tan(u/v), u = 5s + 9t, V = 9s – 5t az as az at

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Q: Use the Chain Rule to find ôz/ðs and dz/dt. z = tan(u/v), u = 3s + 6t, v = 6s – 3t dz %3D as Ot

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Q: 6. Let f(u, v) = u sin(v) – v cos(u) and u(r,y) = r² – ry² v(r, y) = y – r Find af af and both by…

A: We need to find the derivatives using direct substitution and by chain rule . Now , we have ,…