(t, 3t, t ). Find T(t). Use the Product Rule on the product of Let r(t) TETO and r'(t) to get T'(t). You do not need to fully simplify the result. Finally, find T'(t) at t = 1. You must simplify this.

Q: Find the laplace transform of f (t) = te2t sin 2t %3D

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Q: Solve the Laplace Transform of the equation f(t)= sin3t/t

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Q: Find without using the Chain Rule and the ProductRule

A: We simplify the inner function using the properties of log.

Q: x(t) = t³ + 5t – 2 %3D

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Q: Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t = 0

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Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt

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Q: Use the appropriate form of the chain rule to find the derivatives. w = 11x² + 11y² + z²; x = p sin…

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Q: Find the laplace transform of f(t)= { t² 02

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Q: * Q5- Find the Laplace transform for f(t) = ( e5t + sin t )²

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Q: Use the Chain Rule to find dz/as and dz/at. 2 tan(u/v), u = 5s + 2t, v = 25 - St

A: Proceed as shown

Q: sinh 2t (f) t

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Q: Find the Laplace transform of f(t) = t²e7t

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Q: dw where w = cos 8x sin 3y, x=- dt 5. and y=t". Use the Chain Rule to find 2

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Q: 8. x(t) = e2'(t3 + 3t) %3D

A: 8 Given function is xt=e2tt3+3t. We have to find the Laplace transform of xt=e2tt3+3t. Now,…

Q: What is the the laplace transform of  f(t)= 7t +19 +7t2 H(t-6)

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Q: . Find the Laplace transform of the function f(t) = 2t + 3 cos(3t) + 4 sin(3t)

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Q: Solve for the laplace transform x(t) = (t+3) sin(t-6)

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Q: Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t=0

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Q: f(t) = sin* 3t

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Q: - Use the definition to find the Laplace Transform of: f(t) = 4 t. %D

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Q: Find the Laplace Transform of the function f(t) = t2

A: It is known that ℒtn=n!sn+1.

Q: 2 – 2e ª +tU(t – 2) + dt те

A: using laplace formula for finding above laplace values....

Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

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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: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: Find the Laplace transform for 1. f(t)=e*(? +2t +5),

A: As per our guidelines, we are supposed to solve only question.Please repost the remaining question…

Q: Find the Laplace transform of 0, t2 – 8t + 21, t2 4 t < 4

A: the Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that…

Q: Use the Chain Rule to find dw/dt. w = In Vx2 + y2 + z2 ), x = 4 sin(t), y = 6 cos(t), z = 5 tan(t)…

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Q: Find the Laplace transform of f(t) = (t² + 1)²

A: Use Laplace table.

Q: Ex2: Solve by using Laplace transform y'-x = et • x'+y = e=t, where, x = 0, y = 0,

A: The given system is, where initial condition is x=0, y=0. Now taking Laplace transform of equation…

Q: Let z(x, y) 2x2 – 3y? where a 2s – 4t & y = 9s + 8t. he at dy dx az Calculate ds dz by first finding…

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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: 2. Find dy where y = v3x3 +4x + 1.

A: Given y=3x3+4x+1

Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

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Q: Find the Laplace Transform 3.f(t)=(t + 2)²et

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Q: f(t) = 2Ct -4)

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Q: dx Use the chain rule to find () in terms of x and y dy 2 y = ( and X = t2 at t= 2

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Q: Find the Laplace transform of f(t)=u(t− 3)(2t² +1)+2e³ cos²t

A: The objective is to find the laplace transform of f(t).

Q: Find the inverse laplace of (2s-1) F (s) s2 –6s+18

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Q: 3. f (t) e2t Cos 5t 3t3

A: The Laplace transformation formulas are Leatcosbt=s-as-a2+b2,  Ltn=n!sn+1. Substitute a=2, b=5 in…

Q: Use the chain rule to find dz/t. z = x² + y² + xy, x = sint, y = et

A: Here we will find dz/dt,

Q: Determine the Laplace transform of the function f(t) = (t + 2)².

A: We need to determine the Laplace transform of the function: ft=t+22.

Q: 0st<3 f(t) = { f(t) = t2 3

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Q: f(t) = 5te-²t cos(3t)

A: We have to solve the given problem by Laplace transform.

Q: Find the laplace transform of f(t) = e^t3

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Q: Find the Laplace transform of f(t) = e='(t² + 3t + 4)

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Q: Find the Laplace transform of 1. f(t) = sin(4t +) %3D

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Q: Find the laplace transform of f(t)= { t 02

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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: solve using laplace transform: f(t) = sin(t/5)

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