Assume w = x²y*, where x and y are functions of t. Find dw/dt whenx = 3, dx/dt = 2, dy/dt = 4 and y = 1.

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Q: If z = xy + 3xy', where x = sin 2t and y = cos t, find dz/dt when t = 0.

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Q: If x2 + y2 = 100 and dy/dt = 8, find dx/dt when y = 6. (Enter your answers as a comma-separated…

A: Consider the given: x2+y2=100 Differentiate w.r.t. "t",…

Q: dz Use the Chain Rule to find dt for z = x2 + y2 + xy,x = sin t , y = e'.

A: z=x2+y2+xy ; x=sint , y=et

Q: Find the total differential dw. 1 5. w = x tan¬' y – 2ªyz -

A: Solved below

Q: Assume that x and y are functions of t. If y = x² + 4x and dx/dt = 4, find dy/dt when x = 1. dy dt…

A: Solve the following

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Q: Find dx/dt given that 4x^2+9y^2=13x  x=1,  y=-1 and dy/dt = 10

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Q: Let y = f(x), where f(x) = Vx + 4. Find the differential of the function. dy =

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Q: Assume that y=2x and dx/dt =4. Find dy/dt . dy/dt

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Q: If L = √(x2 + y2), dx/dt = -1, and dy/dt = 3, find dL/dt whenx = 5 and y = 12.

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Q: use Separation of Variables to find the general solution. dy/dt= y tan t

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Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t² at t=1

A: I have solved the problem with two methods.Final solution is in the box.

Q: Assume that x=x(t) and y=y(t). Let y=x^2+2 and dx/dt=2 when x=5. Find dy/dt when x=5

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Q: Assume that x = x(t) and y=y(t). Let y = x³ +5 and dt Find dt dy dt when x = 3. (Simplify your…

A: Here is the solution:

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

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Q: Assume w = x2y4, where x and y are functions of t. Find dw>dt when x = 3, dx>dt = 2, dy>dt…

A: Given:  w = x2y4, x and y are functions of t  To Find: dw/dt when x = 3, dx/dt = 2, dy/dt = 4, y = 1

Q: Let x+y = 100,if dx dy = 2, find dt when y-6 and x-8 %3D

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Q: Assume that x = x(t) and y = y = y(t). Let y=x^2+4 and dx/dt =2 when x=5. Find dy/dt when x=5

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Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 6, find dt dy when x = 4. dt (a) If dy…

A: Given y=2x+1 dydx=dydtdxdt

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Q: Let y = f(x), where %3D 7 f(x) = x + Find the differential of the function. dy =

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Q: If L = sqrt(x2 + y2,) dx/dt = -1, and dy/dt = 3, find dL/dt when x = 5 and y = 12.

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Q: Calculate dy/dt using the given information. xy2=4; dx/dt=-5, x=4, y=1

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Q: find dy/dt. y = (esin (t/2))3

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Q: Given: y=fso(x-1) dt - dy =D{(x). dx show that

A: We will prove the following result using Leibnitz rule.

Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

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Q: Assume that y = 5x and dx/dt = 2. Find dy/dt.

A: Consider y = 5xApplying derivative with respect to t on both sides and plugging the values:

Q: If L = 2x2 + y2, dx/dt = -1, and dy/dt = 3, find dL/dt when x = 5 and y = 1

A: Consider the provided equation and information,

Q: Find dy/dx: 1. y = J" cos t dt

A: Given

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Q: Suppose y = V 2x + 1, where x and y are functions of t. %3D (a) If dx/dt = 9, find dy/dt when x = 4.…

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Q: Use the method of first principles to show that d/dt(lnt)=1/t

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Q: Assume that y=5x and dx/dt = 8 find dy/dt

A: Differentiate by chain rule : →f(g(x))dx = d(f(x))d(g(x))×d(g(x))dx.

Q: Find dy/dt using the given values. y = x - 3x for x = 4, dx/dt = 4. dy dt

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Q: . Let y =sqrtx Find the differential dy

A: To find, y=x To find the differential dy.

Q: Find given that dt x² + y² = 2x+4y, x = 3 y = 1, and dy dt i dx dt

A: SOLUTION-

Q: Find dy/dt. y =

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Q: If y = x2 and dx/dt = 3, then what is dy/dt when x = -1?

A: Differentiate both sides with respect to t.

Q: x +y = x2 29) If - х - у + y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0?

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Q: Assume x and y are both differentiable and functions of t. dy when x dt dx = 3? dt If y = x², what…

A: Explanation of the answer is as follows

Q: dæ Let y = 3.75a + 4.75 and dt 0.2. dy dt Find when x = 3,

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Q: Find dx/dt when y=2 and dy/dt=3,given that x^3=9y^3-64

A: Find dx/dt when y=2 and dy/dt = 3, given that x^3 = 9y^3 – 64.

Q: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…

Q: Let W=x*yz.compute the differential dw.

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Q: dr Suppose dx dt dy 4, = 3. Find given that r = dt dt x = 8 y = 2 Write your answer in exact form,…

A: Topic = Derivative