y = x sin-'x + v1-x² What is dyldx? " v1 - x2 x tan-1x >>>> >>> cos-'x sin-'x

Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: 4. y = 5 cos 4x, 3rd derivative 5. y = 3 tan 3x, 2nd derivative %3D 5. y = 6 csc x, 2nd derivative

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Q: Differentiate the function. y= ln(x3 sin2 x)

A: First, we simplify the given function using the multiplication and power rule of logarithm.

Q: cos x 3. y = tan (3x)cot (3x) 4. y = 1+sin x 5. y = arctan (3x5) 6. y = x arcsin x + V1- x²

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Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

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Q: {2xy cosx2 - 2xy + 1}dx + {sinx2 - x2 + 3}dy = 0

A: Simply rearrange the given differential equation and integrate to get the solution.

Q: =) lim cos 3x sec 7x Xー

A: 1) a) The given function is, limx→π2cos 3x sec 7x. limx→π2cos 3x sec 7x=00 Rewrite the given…

Q: Evaluate the integral.

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Q: (tan x) = fu. v dx = (sin x) = | -=-=dx = (cos x) = fe" dx = | (arcsinx) = sec x tan x dx = secx tan…

A: We have to find out derivative and integral

Q: dx (x – 2)Vx² – 4x +3 dx sin-1xV1- x2 L. cos(sec xVx2 – 1 -x) dx 2/V3

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Q: |(sin 3x + cos 2.x)* dx

A: Given integral is ∫sin3x+cos2x2dx

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: sin (2.x) cos (3x) dx

A: Integration:

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: 4 sin-lx dx X.

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Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: 1-sin(x) (1-Sinx)2 10. Find the equation of the line tangent to the graph of y = 3cos(x) at the…

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Q: 4. sin2xcosx + sin x 1 xE[-27, Zn]

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Q: FIN 2 dx

A: Note:- In given problem, according to written way sin2x is multiplied by 3x+1. If you want solution…

Q: 1- x Vx2 + 9 dx. 1 2-5 dx 1+ sinx 3- sin'x cos'x dx

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Q: 5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

A: Indefinite integral is the process through which one can determine the function which on…

Q: 2. Find the derivatives of the folowing equations: y = sin-'(1 -t) y = csc-(x/2) y = In(tan- x)

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: cos x sin x dx 4. sin 2x cos 2x dx

A: In some cases indefinite integrals can be converted to standard integrals using an appropriate…

Q: 1+sin 2 x 1) Find the derivative of f(x) 2 cos3 x

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Q: Differentiate the function y=ln(x5 sin2 x)

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Q: e-V2x sinh x sin x x dx

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Q: (3 tanx-2 cos y)sec" xdx + tanxsin yay = 0

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Q: 1. 2. dx dx sin²(x² + 2x + 1) [4 tan(3x³) - 5 csc x]

A: To find derivatives

Q: 1) y = sin(1 – x²) 2) y = tan 'Vx² + 2x 3) y = tan1 Vt²-1 + csc 1t

A: Given the trigonometric function

Q: 8e cos 2x dx csc(x) sec(x)

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Q: S tanx 1+ COS X JX

A: Given problem:-  ∫tan(x)dx/(1+cos4(x))

Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

Q: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

Q: eCoS ecos x sin x dx In x 2. Vx 3. tan'x dx

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Q: 9) | sin´x-cos'x dx 10) [ cor"/x - dx

A: Solve: 9)  ∫sin4xcos3xdx10) ∫cot2xxdx

Q: tan'x sec x - COS X %3D SBCX

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Q: \ cosx + sinxr cos³x + sin³x 3 3. 3. cos x – sin°x |dx 3. cosx + sinx cosx – sinr

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Q: sin 3x dr + 2y cos* 3x dy = 0 COS

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Q: 4x 3-limx-0 tan5x sin(cos y) 4-lim, y- 2

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Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

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Q: i) etan-¹x 12 1 + x² dx ii) ii) sin sin5 x dx

A: Solve the following

Q: 4 cos °x sin x dx 3x sin: 1/3

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Q: differentiate the function: y= ln(x^9 sin^2(x)) y'(x)=

A: Given function as

Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

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Q: dx 2 sin x - cOS X |tan+ 2 + V5| In 5 tan; + 2– V5 |tan+2-V5 + C + 2+ V5 2. + C In Option 1 O Option…

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Q: 10. f cos*x sin x dx 11. (sec² 3x) dx / (tan 3x) 12. Setan 2x sec² 2x dx

A: Topic:- integration  Note:- as per our guideline if more than three subparts posted than only first…

Q: 2u sec(ux) In|sec(ux) + tan(ux)| dx

A: Consider the provided integral, ∫ 2usecuxlnsecux+tanuxdx Solve the above integral. First, we take…

Q: e) y=sin(tanx) f) y = sin³ 7x

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

A: y=(x – 1)(2x – x2)   +sin-1(x – 1) y'(x)=d(x – 1)2x – x2   +sin-1(x – 1)dx        =d(x – 1)2x – x2…

Q: Cos x dx In x (sin x) () - dæ. (In x)²

A: We have to find the value of the integral : ∫cos(x)ln(x)dx-∫sin(x)1xln(x)2dx