5. Find de for y = 3csc x + x2 dy On= -3ese(#)cot(2) + 1) dy = -3csc x)cot ( x 10 dx O 2) dy 3csclr)cot (7)

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e %3D 5. (x2 - 1) dy =…

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Q: g) y ext= cosh x + √cosh²x -1 +7 ex е X h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy dy -…

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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: 1 To evaluate the integral dx, we (x2 + 2x)3/2 sec 0 1 substitute

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Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

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Q: 1. sin x sin ydx + cos x cos ydy = 0 2. 3 ydx = (3x + 1)dy 3. (х — 2 у)dx + (2х+ у)dy %3D 0

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Q: 3. Find a result by using exact for a. cos(x + y) dx + (3y2 + 2y + cos(x + y))dy = 0 2)dx

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y (In x) 3. y= In(tan x)

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

Q: Q,7 Evaluate the integral 1) L,x* dx 2) xVx+1 dx 3) f cos2xdx

A: we have to solve

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: Evaluate S (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: In(5x +3) dy at x = 0. dx (a) If y = then find et

A: Given; y = ln(5x+3)/e5x

Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

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Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

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Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

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Q: 3. Find dy/dx of: x'(x-y)-x-y evaluated at x = 0.001 and y = 0.002

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Q: 7. What is the order, degree and linearity of: (dy + 3x dx, d°x = ey dx3 8. What is the order,…

A: Note: since you posted multiple questions. As per our guidelines we are supposed to solve one…

Q: Find dy/dx of y=sin-!x+cos -!x dy/dx is Blank 1.

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Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: dy x(2 In x+1) 1. dx siny+y cos y

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: 8. Evaluate the double integral. cos 2x.sin y dy dx

A: Solution-

Q: S2ta J 2tan x In (cos x) dx=

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Q: S tan ax secex dx 3

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Q: 9. Evaluate the integral ex V2e-2x – 3e2x 2/2e-2x – 3e2x +C А. 1 3eªx – 2+C B. 2/3 Arcan V3e2x…

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Q: dz Find dy x sin(2y – 5z) =1+y cos(6zx)

A: Given x2sin2y-5z=1+ycos6zx. To find ∂z∂y.

Q: 4. Evaluate: a) 4 (earctan x)dx o dx b)음 arctan x dx # earctant dt

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 4. Get the exact a. dy = cos 2x dz differentials of y = (sin 2)² b. dy=sin 2z dz dy = sin 2x d.…

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y= (In.x) 3. y = In(tan.x)

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Q: 7 Integrate by using the Archimedes-Riemann Theorem | (2.02 + x)dx

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Q: I. Find dy/dx of the following: 4. y=√1+In²x 7. y In- COS X √4-3x² 5. y = sin²(In x) 8. y In, x- 6.…

A: Topic - Derivative of a function Power rule: ddxxn=nxn-1ddxln(x)=1x

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: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

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Q: 3. Find dy/dx of: x(x-y)-xーy evaluated at x = 0.001 and y = 0.002

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Q: Intergrate dy (2y-x) =In Co)

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Q: Solve the problem. Rewrite the integral 5(1 - z/6) 2(1- y/5 - z/6) dx dy dz in the order dz dy dx.

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y 2logy x %3D

A: we have ,  y=3sec3t and x=etan3t we have to prove that , dydx=(ln3)2·yx·logyx…

Q: 2. Evaluate dy/dx for y= x In x 1+inx

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Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

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Q: dy 1. sin 2ycos2y

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

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Q: 4- Find dy/dx for y = 3[(sin-(e-3x*)1² dy 3(sin-(e-3*)1* In3 2(sin-'(e-3**) 1(-6x) %3D dx V1- e-6x2

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x3/2 from (0, 0) to (4, 8)

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Q: 3. Find dy/dx of: x'(x-y) -x-y evaluated at x = 0.001 and y = 0.002

A: The given equation is x2x-y2=x-y2 at x=0.001 and y=0.002.

Q: 7 Find (b) x siny-ycosx-y = 1. dx

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Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

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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Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

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