Assume x and y are functions of t. Evaluate dt for 4xeY12-In 729+61n x, with the conditions -6, x-3, y0. dy dt (Type an exact answer in simplified form.)

Q: Use the Quotient Rule to compute the following: d/dt (t^2+1/t^2-1) at t= -4

A: The quotient rule of derivative is    ddtuv=vdudt-udvdtv2

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: NOTE: Refresh your page if you can't see any equations. . here we have the given function is

Q: Let r(t) = Find fr(e) de (don't include the +C) fF(t)dt = < [

A: Given,  r→(t)=-4t4-3,-4e3t,-2sin(-t) ∫r→(t) dt =∫-4t4-3dt,∫-4e3tdt,∫-2 sin-tdt

Q: dA find dt dx 1 IfA%3D х? аnd 3 when x = 10, dt

A: our objective is to find the derivative at x=10.

Q: Consider the following. w = cos(x - y), x = t2, y 52 (a) Find dw/dt by using the appropriate Chain…

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Q: Assume that all variables are the function of t. If 5x2 - 4y3+3y=D7 and dy/dt 2 when x-11 and y=3.…

A: Take the derivative of the given equation with respect to t and substitute all the values than solve…

Q: Find f(4) if •f(x) b. a. t2 dt = x cos TTX. f(t) dt = x coS TX %3D

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Q: Assume x and y are functions of t. Evaluate dx = 9, x = 3, y = 0. for 4xe = 12 - In 729 + 6ln x,…

A: Given query is to find indicated derivative.

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: If f(æ) = S Tm dt for x > 1, 1 | In t find f'(2).

A: Please refer the attached image for complete solution.

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

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Q: Consider the following. w = cos(x − y),    x = t2,    y = 21 (a) Find dw/dt by using the…

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Q: dz dS 2 If S = z3 and -2 when z = 3, find dt dt

A: Derivative

Q: Assume that y is a continuously differentiable furction in t Evaluate a) tP (+),A (+)) d tant sect…

A: Given: y is a continuously differentiable function in t. (a) To find: ∫xexπy(t)y'(t)dt

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

A: Given:         8y3+x2=1dxdt=2x=3y=-1 Differentiate 8y3+x2=1 with respect to t,…

Q: Assume x and y are functions of a third variable t. If xy = 20 and d = 10, find dy dt dt x = 4.…

A: u.v = uddx v + v

Q: S. Find f(t), if f'(t) = df 1+ cos(2t) and f =1. %3D %3D dt

A: To find the function f(t) following the given conditions.

Q: Assume x and y are functions of t. Evaluate dt for 2xy - 2x + 4y3 = - 56, with the conditions = -…

A: Given      2xy-2x+4y3=-56 →           1      dxdt=-16, x=4, y=-2

Q: assume that x and y are both functions of t and find the required values of dy/dt and dx/dt.…

A: Given y = sqrt x =x(1) Given x = 9 and dxdt= 2∴dydt= 12x .dxdt by chain rule⇒dydt= 129 .(2) = 19…

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

A: We have the given function in x and y as 2xy-5x+3y3=-51 On differentiating both of the side with…

Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: 4x - 6xy? + 3y² = 228; dx = 3, x = -3, y = 4 %3D

A: Given  4x3-6xy2+3y2=228 ; dxdt= 3   at     x=-3    , y=4

Q: Assume x and y are functions of t. Evaluate for the following. dt dx 3 3, х%3D1, у%3D2 3 '= 2x + 6;…

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Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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

A: w=x2+y2, x=cost, y=sint, t=π, We have to a) express dWdt as a function of t, both by using the Chain…

Q: Assume x and y are functions of t. Evaluate dt y³ = 2x² +6: dx dt -=4, x= 1, y = 2 for the…

A: Please follow the next step.

Q: Find the value of dr / dt at t = 0 if r = (θ2 + 7)1/3 and θ2t + θ = 1.

A: Consider the provided equation, r=θ2+713 and θ2t+θ=1 Find the value of drdt at t=0. Apply the chain…

Q: ) Let w = xe/z, where x =t², y = 1-t, and z = 1+ 2t. Use the chain rule to dz find . (Write your…

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Q: 2 Let F(t) = (+²5¹ √5t – 2, sin (5t)). t-5' fF(t)dt f(t)dt = ([ Find (don't include the +C) + C

A: Above question is solved.

Q: Let u(t) = 2t°i+ (t - 1)j- 8k. Compute the derivative of the following function. %3D (118 + 7t) u(t)

A: First we have to multiply the given function and then calculate it's derivative

Q: Consider the following. w = cos(x - y), x = t2, y = 1 (a) Find dw/dt by using the appropriate Chain…

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Q: Assume that x = x(t) and y = y(t). Find dt using the following information. dy x² +y? = 2.92; - 2…

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Q: x²y – 3yz? + xz, x = t², y = -t, z = t. W =

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Q: Assume x and y are functions of t. Evaluate dy / dt for the following. y3 = 2x 4 + 6 ;        dx /…

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Q: Assume that x and y are differentiable functions of t. For the following, find  dx/dt given that x =…

A: Differentiate both sides with respect to t

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following. y ln x + xey = 1; dx/dt…

A: Solution: Consider the given function is yln x + xey = 1 and dxdt = 5  We have to find dydt at (x,…

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

Q: (a) express dw/ dt as a function of 1, both by using the Chain Rule and by expressing w in terms of…

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Q: Assume that all variables are the functions of t. If 3y2-2x2+4y=2x and dy/dt =2 when x=5 and y=13.…

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Q: Consider r (t) = ( – 4t² + 3, 2e“, 4 sin(5t)). Find F(t)dt. Don't include the +C. frwa = %3D

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Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given xy=6, we need to find values of dx/dt and dy/dt under given conditions. The solution is given…

Q: Assume that all variables are the functions of t. If 3y2-2x2+4y=2x and dy/dt =4 when x-9 and y=12.…

A: Given,  3y2-2x2+4y = 2x   and dydt= 4  when x = 9  and y = 12  Then, we have to find the value dxdt…

Q: dw Use chain rule to find dt if w = xez, x = t², y = 1- t, z = 1+ 2t.

A: Given w=xeyz, x=t2, y=1−t and z=1+2t We have to find dwdt by using chain rule. Hence, by chain rule…

Q: Assume x and y are functions of t. Evaluate dy / dt for 3xy - 6x + 4y 3 = -80, with the

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Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following .xey = 2 - ln 2 + ln x;…

A: It is given that, therefore the time derivative of the given function is, But it is also given…

Q: Assume x and y are functions of t. Evaluate dy over dt for the following. y = 2x 2 + 6 ; dx over dt…

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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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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.