4. A particle path is described by y = 4 cos (2x). dy a. What is an expression for as a function of x and dt b. What is an expression for d²y dt² dx ) -? dt dx as a function of x, and dt d²x dt² ?

Q: dy If dx = COS s 2x, then what is y?

A: The derivative is given by dydx = cos2x                         ........(1)

Q: A. Differentiate each function. 1. y = 2 sin3 n x 2. у %3D csc(x3 — 1) 1- sin x 3. у %3 1+ sin x

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Q: 5. Solve the following D.E to find y as a function of x : d´y +y = 12 e3* +8 dx?

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Q: Compute if df = 2 and dx du dx = 6.

A: It is given that,

Q: d | Vsint dt dx 3 2.

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Q: 49. Let x = 12 + 1, and let y = sin t. (a) Find dyldx as a function of t. d dy (b) Find as a…

A: x = t2 + t        and  y = sint

Q: Determine the value of- dy - at (0,0) for the following expression: 3x² +2y = 3x – 2y dx 10.

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Q: 2. Let y = x? 4x2 . LA. Find "dy". B. Find the value of "dy" when x = 4 and dæ = 0.01.

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Q: Let y = cos(2x) 9x²+3 Calculate dy dx

A: Given function, y=cos(2x)9x2+3

Q: 2. Find each of the following derivatives: d 1 dx x° ,5 d x (י4x+ nא1 (3sin ,3 dx d (7) .3 dx d [tan…

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Q: 4- Determine an expression for dy/dx. 3(y-2)3– x= 4x - 6.

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Q: 10. An airplane flying 390 feet per second at an altitude of 5000 feet flew directly over an…

A: From Pythagoras theorem  for a right angle triangle with base a, height b, hypotenuse c we have,…

Q: Differentiate. In x y= 11 y3D dx

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

A: Given w= sin(8x)cos(4y), x=t/2 , y=t3

Q: 1. Evaluate x + x? (y) dy dx. COS

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Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

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Q: Find the equation of a line normal to the curve of y= cos at x= 1. Select one: A. -33 x + 9y - 9 +…

A: Equation of Normal

Q: Determine the amplitude of the function y = -4 sinx- 7. а. 7 с. 4 b. -7 d. -4

A: Generally the following is the formula used for calculating the amplitude:y = A sin(ωt+ϕ)Where, y…

Q: dy If y=u? and u = x3 + 4 determine dx

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Q: . Which of the following is a property of the function y = Inx? Bln (") = Inu A. Inuv = vlnu C.lnvu…

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Q: 4. In each part below, find dy dx a. y=x³ +5* +55

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

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Q: 2. Determine dy/dx of the following equation. y = a. C. eeez dy dx = dy dx eeez = e. None of the…

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Q: 6. If f(x)dx = 5, f f)dx =2, and , f(x) dx = –1, find i f)dx. а. —2 b. 2 C. -3 d. 3

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Q: Evaluate Set 7x cos (6x) dx. Sex cos (6x) dx =

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