Let w = f(r.0) where r and 0 are functions of s and t, then according to the chain rule is equal to at cv dr dw de Ow or ar as dr dt do dt Ow de ar ôt a0 at Or dt a0 dt

Q: Use the Chain Rule to calculate f(r(t)). dt f(x, y) = x³ - 5xy, r(t) = (cos(4t), sin(5t)), t = 0…

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Q: For the given functions, (a) express dt as a function of t, both by using the chain rule and by…

A: Topic = Derivative

Q: z = (x +y) e°, x = 5t, y = 4 – t2, find dz/dt using the chain rule. Assume the variables are…

A: Given functions are : z =x+yex,    x = 5t ,   y = 4 - t2 By using Chain Rule, dzdt=dzdx·dxdt +…

Q: dw dw For the given functions, (a) express as a function oft, both by using the chain rule and by…

A: SOLUTION-

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:

A: Given: x2+yx-y=9, dxdt=2, x=4 ,y=2, where x and y are functions of t. To evaluate: dydt. Solution:…

Q: Q2/ Express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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Q: Let f(x,y,z)=xy+z and x=st, y=st^2 and z=s^3t^3 (a) Calculate the primary derivatives ∂f/∂x=…

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Q: Consider the functions z = 4 e* In y, x= In (u cos v), and y =u sin v. dz and du dz (a) Express as…

A: Given, z=4exlny,  x=lnucosv,  y=usinv Part (a): z=4exlny,  x=lnucosv,…

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: w = xyz, x = s + 4t, y = s – 4t, z = st2 (a) Find aw/ds and dw/dt by using the appropriate Chain…

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Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x2 + y2 x = 5t, y = 3t t = 2 dw dt…

A: Please refer the attached image for complete solution.

Q: Use the functions below to (a) express dw as a function of t, both by using the Chain Rule and by…

A: w=z- sin xy x= 4t y = In (t-8) z= et-9 To find  (a)  To express dw/dt as a function of t, both by…

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

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: z=(x+y)e^y, x=3t, y=4−t^2, find dz/dt using the chain rule. Assume the variables are restricted to…

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Q: Consider the following. w = xy2 + x2z + yz2, x = t2, y = 8t, z = 8 (a) Find dw/dt using the…

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Q: (a) express dw/ dt as a function of t, both by using the Chain Rule and by expressing w in terms of…

A: Given, 1. w = x2 + y2 , x = cos t,  y = sin t;  t = π  2. w = x2 + y2 , x = cos t + sin t,  y = cost…

Q: dw For the given functions, (a) express as a function of t, both by using the chain rule and by…

A: The solution of the problem is given in the next steps.

Q: Let f(x, y, z) = x'y³ + z³ and st, y = st?, x = and (a) Calculate the primary derivatives af af dy…

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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: Let f(x, y) = x?y? and e(t) = (t, t³) (a) Calculate: Vf•d (t) = d (b) Use the Chain Rule for Paths…

A: Solve by chain rule

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: Let w = f(x, y), x = g(t), and y = h(t), where f, g, and h are differentiable. Use the appropriate…

A: Consider the given functions.

Q: Write a chain rule formula for the following derivative. for w = f(x y.z), X = g(rs,t), y =…

A: We will use chain rule to find given derivative.

Q: By using the multivariable chain rule, compute each of the following derivatives. (b) af/ds and…

A: (b) Given function is fx,y=exy Where, x and y is the function of s and t and defined as x,y=s-t,2st…

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) = 8x + 2y2, r(t) = (cos(t), sin(t)). Use the Chain Rule to calculate f(r(t)). !! dt…

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Q: Consider the following. w = xyz, x = s + 5t, y = s – 5t, z = st? (a) Find dw/s and dw/at by using…

A: Using chain rule and converting function in term of s and t are differentiated.

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: Consider the following. w = xy2 + x2z + yz?, x = t2, y = 5t, z = 5 (a) Find dw/dt using the…

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Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x2 + y2 x = 2t, y = 5t t = 2 dw dt…

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Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x2 + y2 x = 3t, y = 5t t = 2 dw dt…

A: If W is a function of x and y. Also both x and y are function of t then the derivative of W wrt t is…

Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: (a) Consider the provided equations, w=2yex-lnz, x=lnt2+1,y=tan-1t  and z=et ; t=1  Express dwdtas a…

Q: Consider the following. w = xy2 + x?z + yz², x = t2, y= 2t, z 2 (a) Find dw/dt using the appropriate…

A: Topic- differentiation

Q: Use the chain rule. If W=u^3 and U=t-1/t+1, find dw/dt when t=1

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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 following. w = xy2 + x2z + yz2, x = t2, y = 6t, (a) Find dw/dt using the appropriate…

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Q: Consider the following. w = cos(x - y), x - t2, y = 59 (a) Find dw/dt by using the appropriate Chain…

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Q: Consider the following. w - xy + xz + yz?, x= t, y- 7t, z-7 (a) Find dw/dt using the appropriate…

A: We have to use chain rule to solve the question.

Q: dw dw For the given functions, (a) express as a function of t, both by using the chain rule and by…

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Q: Consider the following. w = xy2 + x2z + yz², x = t², y = 5t, z = 5 (a) Find dw/dt using the…

A: Details calculation is given below

Q: Consider the following. w = xyz, x = s + 4t, y = s – 4t, Z = st? (a) Find aw/@s and ôw/dt by using…

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Q: Let w = f(x, y), x = g(t), and y = h(t), where f, g, andh are differentiable. Use the appropriate…

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Q: Let f(x,y,z)=x^3y^2+z^2 and x=s^2t,y=s^3t^2, and z=st^3. (a) Calculate the primary derivatives…

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Q: Consider the following. w = In(x2 + y), x = 2t, y = 8 - t dw by using the appropriate Chain Rule. dt…

A: Solution is given below..

Q: Consider the following. w = xyz, x = s + 2t, y = s – 2t, z = st? (a) Find ôw/ds and ôw/at by using…

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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: 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: Consider the following w-xyz, x s 4t. y-s-4t, z- st (a) Find dw/ds and dw/dt by using the…

A: If F=f(x,y) and  x=g(t) and y=h(t),then     ∂F∂t=∂F∂x∂x∂t+∂F∂y∂y∂t