find / sin³ x cos³ x dx cos³ 2x sinº 2x dx 11. 12. cos² x dx sin? x dx 13. 14. 16. 7 sin y dy 7 cos' t dt 15. 8 sint x dx 8 cos“ 27x dx 18. 17. 8 sin“ y cos² y dy 16 sin? x cos? x dx 19. 20.

Q: dx (2) S V9-x² E(Ctrl) X. 2x sin-1(구)+ sin-1 (민 + Option 1 Option 2 2x cos-1(민 + c CoS Option 3

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Q: Find dy/dx for y = (cos x) 2 + sin(x 2 )

A: Given that      y = (cos x)2 + sin(x2) We have to find dy/dx .

Q: . (4x³y5 sin 3x + 3x*y5 cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A: See the solution.

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: Q1/Prove that S cosh(2x)sinh(x)dx = cosh(3x) – cosh(x)) -

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Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: ind dy/dx of y= tan^-1 (ln x^2

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Q: Find y, of (D² + 1)y = sec x = In |cos x| (cos x) - x sin x В y = x sin x + (cos x) In sec x = x sin…

A: Please see the below picture for detailed solution.

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

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Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: 4. S(cos 2x)e$in 2.x dx 5. S cos x In(sin x) dx 6. ſ tan 0 In(sec 0) de

A: According to given : Only 4,5,6 are solved

Q: (2x-2) dx sinx dx 2. 3. √xdx 4. J² (²2x²+4x-2) dx 5. So (cosx+tanx)dx 1/1/4 6. Jo ¹/2_dx =dx √1-x²

A: Solve by integration

Q: 3y dx 2 (2y In +3 sin y]dy =- + 3 Sin Y X+ 3

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Q: Compute dy/dx if sin(x) = cos(xy^2

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Q: derive ^x dx cos"x Sinx + n-1 Cash Cos"-2x dx n-2, X. Jos"x dx in

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Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: x/2 | (cos(x) + sin(2x)) dx of

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Q: Find dy/dx 1. sin^−1(xy) = cos^−1(x − y) 2. sec^−1(2y cos x) = x^y

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Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: cosxdx 17. - secx+ tan x [2sin(3x)cos(5x)dx 18. [(sin y +2cos y)'dy 19. 20. ſcot'(2x)dx 21. (sin“…

A: solution is given below

Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

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Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

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Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

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Q: 4 sin (2x) dx cos (2x)t4

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Q: 2. Cosh X y sinh x 2 cosh x sin dx dy dxxy = 1 5. (1-x)

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Q: (1-1/2 x^2)cos x 3. y = 2cosxsin2x-sinxcos2x 4. y= x^3 - x^2cosx + 2xsinx + 2

A: Differentiation: 1.y=sinx2+cosxdydx=(2+cos x).cosx-sinx(-sinx)(2+cos…

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x day 6. dx if y = 1-cos4x 1+cos4x dx² dy 7. a if y = In…

A: (7) Let y=lnsinh 5θ and x=cosh(4θ)

Q: Find dy dx In y = e sinx O dy dx O dy dx O dy dx O dy dx = yey sin x =yey cos x = 4 1- ye cos x yey…

A: We can find the answer as below.

Q: 1 point) Find dy/dx by implicit differentiation. 2cos(x)sin(2y)=−4 dy/dx=dy/dx

A: It is implicit differentiation.

Q: -Tsin(nx)cosh(3y) dx + 3cos(7x)sinh(3y) dy =0

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Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

A: Since you have asked multiple questions,we will solve the first question for you . If you want any…

Q: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

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

Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: Whatis the derivative of y = sin (2x − 1)? dx = 2 cos (2x - 1) dy dx = cos 2x dy -2 cos (2x - 1) cos…

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Q: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

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Q: dy Find if y = ln x5 + e-cos 2x – In e?. dx dy 5 ,cos?x-sin2 x dy 5 4 sinx cos x = - dx e sin2x-cos2…

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Q: y = Arctan ( sinh (2x)); y' = * O - 2 coshx /(1+ sinh^2 (2x)) O 2 coshx / (1+ sinh^2 (2x)) O 2/ cosh…

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Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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Q: Q3- Find: 1- Sv2 + sin3x . cos3x dx. 2-5* dx x5-2x sin 2x 2 sin x 4- f cscx cot x dx 4 cos x 5- S 3+…

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Q: 7)(x+tan y) dy sin 2y dx

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Q: 2) Integrate: S(29sinx + 6e + 5 cos x + Vx)dx

A: Given that, The integral ∫29 sinx +6ex +5 cosx+x5 dx By using ∫f(x)+g(x)dx =∫f(x) dx +∫g(x) dx ∫ 29…

Q: Integral of | 4sinxcos cos |dx 1. J sin 9x cos4x dx J cos 2x cos (-x)dx 2. 3.

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Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

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Q: find dy/dx 19) y=Sin" (5x' ) 24) y= Sin 2x.Cos2x 42) y = sinh (tan x)

A: These problems can be solved by the application of Chain rule.

Q: d'y dy dx² dx 21 29 - -6y=6e¹ cos x; when x=0, 20 dy dx =-629 y = 2e-3x - 2e²x 3e-* 29 (3 sin x - 7…

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Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: Given: cosx+tanxy+4=3We need to find dydx.Recall the formulas: ddxcosx=-sinx…

Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

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