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 x dx 4 sin x cos x х Option 4 Option 1 dy 5 4 sin x cos x dy 5 esin?x-cos2 x dx e cos2 x-sin2 x 4 sin x cos x х dx х Option 2 Option 3 + + +

Q: dr dy 2x 3x Suppose x and y are functions of a third variable t. If sin2 (x) + cos²(») = and 1, what…

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Q: find dy/dx.1. y = -10x + 3 cos x            2. y = 3/x + 5 sin x3. y = x2 cos x…

A: Given the functions :- 1.  y = -10x + 3 cos x Differentiating with respect to x dydx =…

Q: dy Find if y = In x5 + e-cos2x – In e?. dx dy 4 sin x cos x dy 5 es sin²x-cos2 x dx e cos2 x-sin? x…

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Q: 1 If f(x,y) = tan-(x y) with x= cos(2 t),y= then sin(2 t) " df can be calculate as follwos: dt O1.…

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Q: Fial dy ldx by imphieit differention. X² (x+y)=y?(7x-y) 2. Find dy /x by implicit differention. e…

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Q: 10. If y zx[sin{inx)- cos(Inx)y find dy/dx. A. sin(inx) B. cos(Inx) C. -sin(inx) D. -cos(Inx) 11. If…

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Q: Q1: A. Find of four of the following: dx 1. y = x sin-1 x +v1– x² 2. y = (x2 + 2x) tanh(x + 1) 3. y…

A: See the details solution in below

Q: dy Q3) Find dx y = (cosx)v2 y = 3tanx In3 2 - e = ylnx 4 - y = cot-1! 1- 3 - + tan-1x 5 - y = =…

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

Q: If xy+sin y = x², then . dy х — 2у - || dx y + cos x 1. dy 2х — у - dx y + cos x 2. O dy 2х — у ||…

A: Proceed as shown below...

Q: dy = [cotytant cosx dx cosy A siny?= sin2xln(csinx) (B siny= sinxln(csinx) siny= sin2yln(csin?x) D…

A: There is something missing in the given answer list.So The solution with correct answer is given as…

Q: dy If y sin(cos.xr), then dx O 6x sin x' cos x O sin x cos(cos x) 0-sin x cos(cos x) O 3x sin x %3D

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Q: Q3 Find and show the work for (x+3)(3x+2) dx. (a) х (b) F (sin(2x) – cos x) dx. (c) S(3x² + 2x +…

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Q: H.W.4 Find dy/dx for the following: 1) y= x+ sin x + sin 5x 2) y 32x + In (sin x) + In(sin 5x) 7) y…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Determine dy/dx given that y = 1+sin x COS C 1 O (1+sin x)² -1 O 1+sin x 1 O 1+sin x -1 O (1+sin x)²

A: The objective of the question is determine the derivative of the given function and choose the…

Q: dy No need to simplify. dx A. Find 1. 2x sin y = (2x + 3y)° 2x' 2. sec (2x – y) – Va = sin* y - 5 3.…

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Q: Q2: Find dy/dx for the following function: (1) y = In(r + 4) -x tan (4) y = x+1) (2) xy +xy = x+ 3y…

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Q: f SSR5e -27 sin(5x)y cos(2y) dxdy = f, 5e-2¹ sin(5x) dx f2, y cos(2y) dy where R = [-1, 1] x [1,2].…

A: This is a double integration problem

Q: Q1) Lind dy/dx of O xe 1o X +3y = 0 2 2sinx cosy=1 9 x = sec!

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: dy ycos³x + y² sin x dx (cos? x sin x + 2y cos x) A O 1/(cos a) .B 2sinx/cosx .C No integration…

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Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

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

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Q: dy Solve for dx sin y+ysin x given xsin y- y cos x = 5 А. cOS x+x cos y sin y-ysin x B. COS x+x Cos…

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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: dy Find dx е 6х 3 sin (x + 5у) %3D ,6x e O A. 5 cos (x + 5y) 6 e 6x - cos (x + 5y) OB. 5 cos (x +…

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Q: IFND HWERE dx dy f(x) = sin-(sinx) dy = 1 A) dx dy 1 B) dx 2 dy 1 C) dx V1 - sin?x sin?x dy D) dx…

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Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A sin x B sinx cosy =…

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Q: dy + 4 (X-11² Y = X+1 cos y dx + (x Siny - cos²y) dy = o 0 9. (x-1)³ [X-11³

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Q: Find dy/dx for the following: 6. (sinvx csc Vx) 9) y* = sin-1 x 8) у%3D 10) y = xtanx + sin-ly 11)…

A: Solution: Hey, since there are multiple questions posted, we will answer first question. If you want…

Q: Solve the DE Ssinx siny dx + cosx cosy dy = 0 by separation of variables. sin y A cos X B sinx cosy…

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Q: 1. sinx siny dx + cosx cosy dy = 0 %3D 2. [2xy cos(x2) – 2xy + 1]dx + [sin(x²) – x²]dy = 0 3. y?dx +…

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Q: Find the dy/dx if y = ett O e** (1 + Inx) Ox*(1 + Inx) et*x*(1 + Inx) O e*(1 + Inx) Find the dy/dx…

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Q: dy Find as for y = x - x sinx O 1) - 1 - 3x² cosx - x³ dy sinx dy O 2) = 1 - 3x² sinx - x³ cosx °…

A: Differential

Q: 4) (2x + y cos xy) dx t x cOs xy dy - o cOs xy) dx t X COS Xy dy COS

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Q: Н. W.4 Find dy/dx for the following : 1) y = x3 + sin x? + sin-1 5x 7) y = 3m (sec2x) eln(cos"*) 6…

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

Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In ( 1 + (Inx)2 + (In vx) 3 3x 2) y = tan-1…

A: Use formula of derivative  to solve

Q: Find . dy dx e 4x, = sin (x + 8y) %3D O In sin (x + 8y) 4e4x -1 S cos (x + Sv) S cos (x + Sv) 4ex -…

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Q: Find the differential dy: y = sin(x√³). Ody = COS cos (T√²³) [2√T™- 2 O 0 O (E) None of these…

A: A detailed solution is given below.

Q: Find dy/dx for the following : 7) y = 3ln (sec2x) eln(cos-1x²) sin/x 8) y = csc Vx 9) y* = sin-1 x…

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Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: find (In x)³ dx 2x In (In x) dx x In x 11. 12. In9 et/2 dx tan x In (cos x) dx 13. 14. In4 eVi cdr…

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Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages Fuse When:x = 0; y…

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Q: 5) (D de with constant coefficients G 6) (D-6D+9)y= Ans.: y=Ce" +C,ue" +*. 7) (D' + D)y = tan x.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 1 If y = sin' x then is dx dy dy -3 cos x b) dx a) –3 sin² x cos x dx sin¯ x dy dy _ -3cosx = -3…

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Q: Can you please check my work for question 14? I know it it hard to follow, but I don't know if I got…

A: The given equation is,

Q: Find dy/dx. y = x' sec (-). A 1 sin 3x cos + x sin2 5x (e) B) x sec 5x sec C) x sec sec D x sin 5x…

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Q: 7. (cos x+xcost)dt +(sin t -t sin x)dx = 0 Ans. t cos x+x sint c 8. (ysin x+xy cos x)dx +(xsin…

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Q: dw Find dx where w = cosz- cos 4x cos'4y + sin 4x sin 4y and z= 4x+ 4y. dw 口

A: lfirst put value of z and then expand cos term Now we get Zero whose derivative is zero

Q: 10. * S sin(In x)dx 1 C x sin(Inx) – cos(Inx) + C 2. x sin(Inx) – cos(lnx) + C 1 x sin(lnx) +…

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Q: 1. Integrate by parts and evaluate x cOS x dx 0, а. b. In(x²) dx 1 In x dx x5 С.

A: By using Integration by part  ∫udv=uv−∫vdu

Q: III. EVALUATE THE FF. ITERA •rU/2 ptan y sec y 1. . x' cos ydxdy Jo . cosy sin2x dy dx xp, •3n /2 pn…

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