9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

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: What is the formula for integrating sin 40 cos 20d0 ? S (sin 60 – sin 20) do S (sin 60 + sin 20) de…

A: SOLUTION-

Q: Find the first derivative of  y = (x – 1) √ (2x – x2)   + arcsin (x – 1), and y = arctan [ (3 sin x)…

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Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

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Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

Q: S sin (2x – 1)cos (2x-1)dx (2х - 1)dx

A:

Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: 3. find dy/dx of y= sinh 2x

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Q: find /x – x² - dx xV4x – x² dx 9. 10. х dx dx 11. 12. xV7 – x² xV7 + x² Vx² (4 x² 4 dx 13. 14. х sin…

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Q: 1) [(sinh 2x + cosh2x)° dx

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Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

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. S. 2 cotx-3 sin²x dx sin x 4. (2x2+x dx x+1

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Q: - sinx) dx 2. 1. (COSX (ax' +b)*x dx 2. 2/3

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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: S" sin" (0.5x)cos (0.5x)dx

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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: Bind dy, 4. Ssinx.cosx sinx-coSX 1 +2.Ln X

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Q: Find dy/dx in terms of x and y if cos^2(9y)+sin^2(9y)=y+7 dy/dx=   implicit derivative problem.

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Q: 1. cos(xy) + secy = 5 2. Arcsin(x/y) = 4x + 3y 3. 4ln(Arctan x) = 1- y 4. y = 5/(sin3x +cos3x) 5.…

A: we have to derivative two times

Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: 2. Integrate using Trig: cos° x dx

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Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: 5. Find where y = In(cosh(2x)) + /sinh-1(2x) + tanh² (7x). dy dx

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Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

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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: 9. . sinh 3x dp- 1+cos 3x 2x+9 10. S x² +6x-4

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Q: 1 3), sinh(x)-cosh(x) dx

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Q: Use differentials to estimate sin (π/6 + 0.01).

A: Use differentials to approximate the value of sinπ6+0.01 The nearest number to sinπ6+0.01 whose sine…

Q: ind the equation of the line that is tangent to y = 2x + sin x + cos x at x = 0.

A: NOTE: Refresh your page if you can't see any equations. . take x=0 the point on the graph is

Q: dt dx 3. 6x – x² 4. sin xV1 XN Cos xdx 3x 5. 1-2e3*) 6. dx

A: We solve only 4th question.  Let 1-cos(x) =t

Q: solve  sin(x)dy/dx + ycos(x) = cos(x)[ex + sec2(x)].

A: Convert into dy/dx+p(x) y=Q(x)

Q: Find dy/dx by implicit differentiation. 5y sin(x2) = 9x sin(y2)

A: Given :  5y sin (x2) = 9x sin (y2)

Q: 4. S tan x dx CSC X sec (In x) dx 5. dx 6. S; 1- cos 2x

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Q: x' sin 2x dx -3x 5. X cos 2x dx

A: We solve these integral by u.v formula of integration

Q: sin 6x dx sin23x 4. 6. S Ve3x + e 4x dx ex dx 8. J 1+ e2x

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Q: 2. Solve (sin y – 3x² + 5)dx + (y +x cos y)dy = 0. (Test for exactness and solve)

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Q: Evaluate the integrals

A: Given integral is:

Q: Integrate: S dx sin ³x cos6x

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Q: 4) S tanx dx cosxv1+secx 5) S(1- u)Vūdu

A: (4)  First we integrate this ∫tanxcosx1+secxdx

Q: Find explict solution of the foilowing initial-value problem dy yoanx?, yla)of %3D dx

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Q: how do i implicitly differentiate (solve for dy/dx) where: xy = tan(xy)?

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Q: 29. (csc x – sec x)(sin x + cos x) dx find + In 5 ) dx 30. 3 sinh .3 2x3 V1 + x² sin x dx 32. 31. dx…

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Q: 4) [ sinh 2xdx 5) [ e* sin e"dx 6) fcosh'vdv

A: Given:  4) ∫0π2 sinh(2x)dx5) ∫ln(π)2exsinexdx6) ∫cosh2vdv

Q: 1 dy if y = dx -1 Find - tan 3x. dy dax

A: Use derivative formula