a)Let z = x?y – y² where x = t2 and y = 2t . Find dz/dt at t=1 using chain rule.

Q: Find dw/dt using the appropriate Chain Rule. Evaluate dw/dt at the given value of t.

A: The given equation is . Also .

Q: Find dw/dt using the appropriate Chain Rule. Function w = x sin y x = e", y = 1 - t Value t = 0 X =…

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Q: b) Use Laplace transform to solve the system of differential equations dr 4y, dt dy dt +x = y + 3e*,…

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Q: Use the Chain Rule to find dz/dt if z= (x+y)e^x, x= 2− t^2, and y=t

A: Given that: z=(x+y)ex,      x=2-t2 and y=t

Q: Let y = 5a. Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4 and…

A: According to question given y=5x2x=4 and ∆x=0.4We have to calculate the change in y, ∆y

Q: Let w(z, y, 2) = x² + y² + z² where z = sin(7t) , y = cos(7t), z = e'. dz dy dw by first finding dt…

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Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

Q: dz Suppose that z = x³ – 3y?, x = 4(t³ – 1), and y = Int. Find using the Chain Rule. dt %3D -

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Q: Use the Laplace transform to solve the differential equation: y' – 2 +y = e', y(0) = 0, y (0) =

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Q: Compute dy/dx using chain rule where y = (u^2+2u)/(u+1) and u = x(x + 1)

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Q: dz Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

Q: Use the chain rule to find dz/dt or dw/dt.  Z=sinxcosy, x=t^(-1/2) y=1/t

A: First of all, put x and y in the form of t and get the value of “z” in the form of “t” only.

Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

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

Q: Find aw/at using the appropriate Chain Rule. w = x sin y x = e', y = - t dw dt

A: Derivative

Q: z = sin x cos y, = VE, y = 1/t x =

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Q: use an appropriate form of the chain rule to find dz/dt. z= 8cosx-sinxy; x=1/t, y=3t

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Q: use the chain rule to find dz/dt, where z=x sin y, x=t^5, and y=5t^2 please show steps

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Q: Let y = 4x. Find the change in y, Ay when x = 5 and Ax = 0.3 Find the differential dy when x = 5 and…

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Q: Use the Chain Rule to find dz/dt. dz dt || z = √√√ 1 + x² + y², x = 2 In(t), y = cos(t) 1 √1+ (Int)²…

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Q: Use chain rule to find dz/dt z=cos(x+2y), x=6t^3, y=7/t

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Q: Let z(x, y) = x'y where x = t° & y = t°. dz by first finding dt dy and using the chain rule dt dx…

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Q: dw Use the Chain Rule to find dt w = x²e²y cos(32), x = cos t, y = In (t + 2), z = t

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x).

Q: Use the Chain Rule to find dw/dt. In(Vx² + y² + z² ), x = 3 sin(t), y = 5 cos(t), z = 6 tan(t) W =…

A: We have to find the derivative  using chain rule.

Q: Let z(x, y) t° & y = 1+ 6t. = xe9 where x = dy and using the chain rule. dt dx dz by first finding…

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Q: ]If x' +y +z =9, dx/dt 5, and dy/dt 4, find dz/dt when (x, y,z)=(2,2,1).

A: Topic- application of derivatives

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: Use the Chain Rule to find dz/dt or dw/dt. z=sin x cos y, x= √t, y=1/t

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: = xy³ + x2y, x = 31- 8, y = 4t2 - 4. dw when t 1. dt Use the Chain Rule to calculate dw dt

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Q: Let z = x?y + 3xy+ where x = sin 2t and y dz find = cos t. Use the chain rule to when t = 0. dt

A: See solution below. Using definition of chain rule.

Q: Use the Chain Rule to find dw/dt. w = In Vx2 + y2 + z2 x = 2 sin(t), y = 5 cos(t), z = 4 tan(t) dw…

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Q: Use an appropriate form of the chain rule to find dz/dt 1. 2 3xy; a r-t' and y

A: use partial derivative for finding drivative.

Q: Let y = 4/r. Find the change in y, Ay when x = 3 and Ax 0.2 Find the differential dy when x= 3 and…

A: We know that, Δy= y(x+Δx)-y(x) Given, y= 4√x --------equation 1 x=3 Δx= 0.2 Therefore, Δy=…

Q: Find dw/dt using the appropriate Chain Rule. Function w = x sin y x = et, y = π - t dw dt || Value t…

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Q: Use the Chain Rule to find dz/dt. z = x2 + y?, x = cost + sin t, y = cos t – sin t. -

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Q: If = Z sin x = 2t, y = 2 – t2, find dz/dt using the chain rule. Assume the variables are restricted…

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Q: Let z = x*y + 3xy* where x = sin 2t and y dz find = cos t. Use the chain rule to %3D when t = 0. dt

A: z=x2y+3xy4where x = sin 2t and y = cos t We need to find dzdt when t =0 Let's use the chain rule :…

Q: Let y 3T. Find the change in y, Ay when x 2 and Ax 0.3 Find the differential dy when a 2 and da 0.3

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Q: Use the Chain Rule to find dz/dt. z = x2 + y2 + xy,    x = sin(t),    y = 3et

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Let y = 4/T. Find the change in y, Ay when x = 4 and Ax = 0.1 Find the differential dy when x = 4…

A: Given:- f(x) =4√x To find :- Change in y , Δ y when x = 4 and  Δ x=0.1  Differential dy when x= 4,…

Q: Let y = 4√x. Find the change in y, Ay when x = 2 and Ax = 0.1 Find the differential dy when x = 2…

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Q: Using the Chain Rule, find dz/dt for z In(x? + y²) and x = t, y = t²

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Q: Let y = 3/. Find the change in y, Ay when x = 1 and Ax = 0.1 Find the differential dy when x = 1 and…

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Q: x²y + 3xy where x = sin 2t and y = cos t. Use the chain rule to dz when t = 0. 3. Let z = find dt

A: According to our guidelines we can answer only first question.

Q: given z= f(x,y), where x = g(s,t) and y = h(s,t). chain rule for dz/dt is

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Q: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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Q: Use the Chain Rule to find dz / dt or dw/ dt.(odd) z = xy3 - x2y, x = t2 + 1, y = t2 -1

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Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.

Q: Let y = 3x². Find the change in y, Ay when x = 1 and Ax 0.1 Find the differential dy when x = = 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…