arcsin 4y dy 1 – 16y2

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: find dy/dx in terms of x and y if arctane(x^3 y)=xy^3

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Q: siny dy 2. 3 |- cosy

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Q: (х+ siny)dx+ (хcosy— 2y)dy 3D0

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Q: Use Fubini's Theorem to evaluate .2 -dx dy. I + xy

A: Given :            ∫02∫01 x1+xy dxdy By Fubini's theorem, the above integral can be rewritten as ∫01…

Q: Prove that (arccsc x) dx d d %3D (csc-1 x) = %3D - dx Ju/Vu2-1

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Q: Differentiate: y = arcsin + Oy = y = - 4-x O y = x V4 – x2 4-x2

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Q: dy 3. 1+ sin 4y

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Q: 2. dx Ix Also, Prove that 22 %3D dxdj = dy dX

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Q: Find general soulution (x+1)dy/dx +(x+2)y=6xe^-x

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Q: Find y': y arcsin Oy =-- %3D Oy = - zV-9 %3D Oy = %3D zV-9 %3D -69

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Q: et secydx + sinydy = 0

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Q: Find fy ) for (x,y) Cos (x) sincy) exy

A: Given query is to find the partial derivative of the expression with respect to y.

Q: I. Find dy -and simplify the result whenever possik dx 1. у%3Dsec3 2х - 3sec2x 2. y = sin (x + 4 )…

A: Given; 2) y=sin(x+4) cos(x-4) 3) y= -3 cot5(x/3)/5 + cot3(x/3) -3cot(x/3) - x.

Q: EXERCISE 1 dy -dx = 0

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Q: -1 Suppose y = sin ¹x. Then y arcsin 1 Oy= sin a Or = siny Or=

A: Given that:- y= sin--1x. Then  Topic:- inverse trignometry

Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: 6.) y'of y = Insin(arctan 3x)

A: This is a basic differentiation question

Q: Integral of sin^3 y cos^5 y dy

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Q: Differentiate y = arcsin(2x + 1) y’

A: Given data: The given expression is y=arcsin(2x+1). The expression for the differentiation of the…

Q: Siny dy = Cas y (l-x Cosy) Cauy) %3D

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Q: (2y) dy. CSC

A: We will start with the substitution, csc-1(2y) = x and apply the integration by parts. And, will use…

Q: Find dy/dx in terms of x and y if arcsin(x'y) = xy". dy dx Submit

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Q: 4In(Arctan x) = 1-y

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Q: 1) y = Arcsin(1 – x²) 2) y = Arctan Vx² + 2x 3) y = Arctan /t²-1 + Arccsc t

A: Given : 1) y = Arcsin (1 - x²) 2) y = Arctan (√x² + 2x) 3) y = Arctan (√t² -1) + Arccsc t

Q: sin(6y) sin(8y) dy.

A: Topic - integration

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: Find dy if arctan(x + y) = xy-

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Q: Find the arclength of y = 3x + 1 on 0 <x < 3 %3D

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Q: 3. у?dx— x(2х + Зу)dy %3D -

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Q: Cos y dy 1-siny

A: The given integral is: I=∫cos2y1-sinydy   As we know that; The trigonometric identity: sin2x+cos2x=1…

Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

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Q: sin y cos(cos y)dy

A: We have to evaluate the integral: ∫sin y coscos ydy In this case we will use substitution method. So…

Q: 2Linear edluotion 5. dy dx

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find dy/dx in terms of x and y if arcsin (x2y)=xy2

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Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

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Q: (d) Differentiate arctan(3v) arcsin(7v) + v² g(v) = In %3D

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Q: dy dx 118 (x = 3x - 5

A: Topic:- differential equations

Q: dy Use an appropriate technique to find dx from x² + y² = (2x² + 2y² -x)*.

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Q: 12) / Зy sin(5y?) dy

A: Solution:

Q: (a) If f(x.y) = e siny - e sinx then verify that fry fyz- %3D

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Q: 2olue dy %3D

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Q: Find the solution. 7. (3siny – 5x)dx + 2x2cotydy = 0 hint: let z = siny

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Q: dy 1+ sin 4y

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Q: 1- x 30. y= arctan V %3D 1+x

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Q: Find dy/dx in terms of x and y if cos² (4y) + sin“(4y) = y + 8. %3D

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Q: Find dy/dx: rsinx 1. у %3D Sm* 3t2 dt

A: I am attaching image so that you understand each and every step.

Q: sin(20nnt) ass A: AS(t)ln:0dd En=1 %3D %3D1

A: