find 3 sec“ 3x dx sec4 0 do 41. 42. csc“ 0 do secó x dx 43. 44. 7/4 4 tan³ x dx 6 tan“ x dx 45. 46. -T/4 tan x dx cot 2x dx 47. 48. 8 cot“ t dt cot³ x dx 49. 50. T7/6

Q: siny dy 2. 3 |- cosy

A:

Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: sec?x Integral tanx

A:

Q: tane cote +- = sin0 + cose %3D 9. Sece csce

A:

Q: Integrate (sinx + cos^2x)^3 dx

A: To evaluate: ∫sinx + cos2x3dx Let I = ∫sinx + cos2x3dx ⇒I =…

Q: Integrate: S tan (æ) sec³(x)dx

A:

Q: sen z + cos x dz | (tag z + 1) dx = In sec x+z + C 37. %3D cos 2

A: 37.   Given integral, ∫sen x+ cos xcos xdx

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: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: Evaluate

A:

Q: What is the integral of question 23 and why is the answer 0?

A: Let f(t)= t^4*tan t/(2+cos t)

Q: 2xycosx^2 -2xy+1}dx+{sinx^2 -x^2 +3}dy=0

A:

Q: et secydx + sinydy = 0

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Q: a) Differentiate f(x) = sin x from first principtes. %3D

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Q: '1+tanx Evaluate the integral 1-tanx dx A In sinx-cosx + C B -In cosx+sinx + C C -In cosx-sinx + C D…

A: Here, to evaluate: ∫1+tan x1-tan xdx

Q: d arctan (tanh x) dx Show that sech 2.x.

A:

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: cos (In z) sin (In x) dx

A: To Evaluate the integral

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

A:

Q: Find of xy = cot(xy) dx

A:

Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: 6. S sin (3x – 1) dx. cos Vi dx. 7. Evaluate th dx. Show yo 8. 3 dx. S (! + 1)(t – 1) dt. 9.

A:

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: Find dyldx y =-secu, u = x- COs X dy -sin(x-cos x) cos x) sin(x-cos x) cos(x - cos x) sec(x- %3D dx…

A:

Q: (ups" = (In tanx) (x*) ( Sinx) (Ny)" sec"('s %3D 2. %3D

A: Here we apply logarithmic differentiation for both Questions

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: dy Find by implicit differentiation. dz 3+ 5z = sin(ry) dy

A: We can find the answer using implicit differentiation as below.

Q: S tan ax secex dx 3

A:

Q: Solve (1+siny)dylx=[(2ycosy-(secy+tany)]dy.

A: This question is taken from a differential equation in which we have to solve the equation and take…

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

A: It is implicit differentiation.

Q: sinx siny dx + Cosx cosy dy = 0

A: Given: sin⁡xsin⁡ydx+cos⁡xcos⁡ydy=0 ⇒sin⁡xsin⁡ydx=-cos⁡xcos⁡ydy ⇒dydx=-sin⁡xsin⁡ycos⁡xcos⁡y…

Q: 2cosx dx 5- f 1+(sinx)2 a)2 tan sinx| b) 2 In sinx| c)2 In(1+ (sinx)1

A: We use Trigonometry substitution method

Q: Show that arctan(tanh(x)) = sech(2x). arctan(tanh(x)) dx D²tanh(x)) %3D 1 + ])-: 1/cosh²(x) 1 +…

A:

Q: Sinhx cosy dx = coshx siny dy

A:

Q: dy =Cos x Sinx cotX 8-

A: As we know that; The standard form of the linear differential equation; dydx+Py=Q Where P & Q is…

Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: Differentiate y= arctan sinh x. coshx A. 1-sinh x cosh x B. cosh x C. ainh-x D. 1+sinh-x

A:

Q: cos(xt) cos (sin(at)) dt D. tan x dx =

A: The question is taken from the calculus in which we have to find the value of the given integral, We…

Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: Find dy dx if sin(x + y) = tan(xy)

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Q: 37. cos 6x dx 40. sin x? dx 39. cos do 42. tan x sec² x dx 41. sin 2x cos 2x dx csc2 x dx cot x sin…

A:

Q: FIND dy/dx FOR EACH FUNCTION. 1. y = (tanx + sinx)-3

A: 1). Given y=tanx+sinx-3. To find: dydx Solution: Power rule of differentiation states that:…

Q: 10.y = Arc cot (sinh3x) 11. y = cosh?4x - cos 12. y = In (sinh4x) cosh8x +x² 2

A: To find dy/dx: 10.y = arc cot ( sinh3x ) dy/dx = [1/(1+sinh23x) ]( cosh3x) 3  = (3 cosh3x) /…

Q: Estimate tan (0.5) using the tangent line to y = tan(x) at x = π .

A: The slope of the tangent if dy/dx at x=π So the slope=1

Q: find tan x dx x² x² tan¬' x dx 19. 20. sin 3x cos 2x dx 22. sin 2x cos 3x dx S sin sin 8 sin 4t sin…

A:

Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

A:

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: dz 5 – 2x cos 2x dx 1 + sin 2x sec² 0 de. tan 0

A: