dy It is known that dx 2x Starting with x² = -2 + y + 5 cos y , show how %3D 1–5 sin y dy 2x is derived. %3D dx 1-5 sin y

Q: cos’x sin x dy + (y cos³x – 1) dx = o %3D

A: We have to find the solution of given differential equation

Q: 7. Find dy dx (a) y = (x* + 5x) cos 5x, %3D

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Q: dy dzy B) Find and if x = sin? 3z and y = tan 3z dx dx2

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Q: 1.Given x=3( θ-sin θ) and   y=3( 1-cos θ) a. Find dy/dx b. Find d/dx2

A: Given: Given x=3( θ-sin θ) and   y=3( 1-cos θ)  a. Find dy/dx  b. Find d/dx2

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

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Q: (e* sin y – 2y sin x)dx + (e* cosy + 2 cos x)dy = 0

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Q: 1 + cos x – 2xy): fip y(y + sin x), y(0) = 1. COS I 1+ y? dx

A: To solve the given exact differential equation.

Q: :? If sin(x +y) = xy, what is the correct expression for dx cos(x+y) - y x- cos(x+ y) A cos(x + y) -…

A: for this problem, we can solve this by using general implicit  differntiation.

Q: 3.S dx C. ez? D. ex А. х В.-х? cos x 4. S9 dx V1+sin x A. V1+sinx B. cosx C. sinx D. 1+ sinx

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Q: (x sin? - ycos) dx + xcos dy = 0. 3. xcos: 4. x²dy + (y2 – xy)dx = 0. %3D

A: 3. It is given that, Take x common throughout the equation and vanish it.  Now let  yx=ν Therefore,…

Q: It / 2 pcos x T-X sin(x + y)dy dz dx Jr/6 JO

A: Let's find.

Q: dy : Find the for the following functions: dx 1- y = e(x+ln 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh x

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Q: dx 16. S sin Ex di √x u= √√x du= I u 12/12 dx = ५५ -1/2 dx 2 би du YN

A: Solve the integration

Q: 1. cos?x sin x dy + (y cos³x – 1) dx = 0

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Q: Evaluate xy dx + (x + y)dy along the curve y=x? from (- 3,9) to (- 1,1). | xy dx + (x + y)dy =|…

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Q: dy in y= sin x Find dx 1+cos x cos?. а. 2 x+ sin x +cos x 2 cos x+ sin? x b. (1+ cos x) 2 (1+ cos´…

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Q: DAVAO dx 1. S( ax² + b)²/3 x dx DAVAD 5x - 2x +3 3. dx 2. S(sin + cos) dx x+a x+b 4. S( cos x – sin…

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Q: 3. sec x tan y dx + see y tan x dy = 0.

A: The solution for the asked part is given as

Q: sin y dy dx If 1 for some a > 1, then the value of a is y 0 x

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Q: dz and dy dz Find 2° In (1+ xy

A: Given that:  z = x9 ln( 1 + xy-5/6). We find dz/dx and dz/dy. Here i attached solution of this…

Q: y -y sin X+ x cos y dx + x sin y dy = 0 is given by A+Bcos y s 2 = 2x . Find A and B.

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Q: dy 4. If y = tan-1(cos x), then dx - sin x А. 1+cos? x B. -(sec-1(cos x))² sin x C. (sec-1(cos x))?…

A: If y=tan-1cos x, then we have to find dydx.

Q: dy If x = a (0 – sin 0), y= a (1– cos 0), then find dx |

A: Introduction :

Q: {[1+ y?] sin(xy) + xycos(xy)}dx + {[1+x²] cos(xy) – xysin(xy)}dy=0

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Q: y = Vx³ + 3 dy Find dx dy dx Type sin(x) for sin(x), cos(x) for cos(x), and so on. Use x^2 to square…

A: ddxx3+3Apply chain rule:=12x3+3ddxx3+3=12x3+3· 3x2Simplify:=3x22x3+3

Q: (sin(æ) + 2 cos(y)) dy ^ dz + (zổ – y cos(x)) dz A dæ + 11xyz dx ^ dy. Find dw. dw dx ^ dy ^ dz

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Q: 3. x = y – y? sin x dx dy sin x

A: Given differential equation x(dy/dx)=y-y^3sinx Now we have find the solution as shown below

Q: du = 3 and dx dy = cos u, find the du dy Given y = sin(3x – 2). If dx 3 cos(2x) 3 cos(3x) 3 cos(3x –…

A: Topic:- derivatives

Q: 3 sin(y) Let h(y) 2+ cos(y) COS d. Determine dy %3D

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Q: dy 1. cos? x sin x+ (cos³ x)y = 1 dx 2. (x + 1)+ (x + 2)y = 2xe™* dx

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Q: h) (3X 9'+4y)dx + (3 X'9 +2x) dj = 0 I) sin X dy dx Sin 2X -y cos X

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Q: 1. Given: y = -2x2 + 5x + 3 Find: S,y dx 2. Given: y = tan (x + 5) -2 Find: Sy dx

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Q: Find dy/dx of y=sin-!x+cos-4 dy/dx is Blank 1. Blank 1 Add your answer

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Q: Find dy and simplify whenever possible. dx sec x+tan x 1. у 3 sec x-tan x 2. у 3 е * соs e * — sin e…

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Q: dy of the following. dx A. Find 4. x cos y = sin(x – y)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 5 (2xy* + sin y) dx + (4x²y³ + x cos s y) dy = 0 %3D

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Q: Here, the function y (x) is defined implicitly: x = cos (a³ + y°). Again, a represents a constant…

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Q: 4. Find d?y/dx² for the following functions: a) y = sin x² cos 2x b) y = cos*(sec² 3x) c) y = x²(x³…

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Q: dy Given dx 3 cos x + 2 sin x. find y. %3D A. -3 sin x +2 cos x + c В. 3 sin x-2 cos x +c C. -3 sin…

A: Integration

Q: 1 dy ( = y(y + sin x), y(0) = 1 + cos x 2xy 1+ y? dx

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Q: dy . If sin (x + y) = xy, what is the expression for xY, dx cos(x + y) – Y - 1- x cos(x + y) – Y - В…

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Q: 11 sin y Evaluate the integral e" cos y dx dy. NOTE: Enter the exact answer. 11 sin y e" cos y dx dy

A: The objective is to evaluage the integral.

Q: äbäi 14 Q) Find dy/dx of the following :equation (x' +x)(x° - x +1) y = 17 KB/S dy/dx = - 4/x^2 O…

A: We use the Quotient Rule and  Product Rule of differentiation to find the answer of the given…

Q: dy for the given functions. dx Q.10 Find 1. y = Vx' - 12x + 5 2. y = In(cosecx) Page 6 of 12…

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Q: if sin(x+y)=xy, what is the correct expression for dy/dx? a. cos(x+y)-y / 1-x b. cos(x+y)-y /…

A: The given function is sinx+y=xy.

Q: sinx b) Find dx if m t2 + 5 dt + cscx + y = x cosx 10 b) Find for sin?x + cos?y = dt xtany t+2 dx

A: b) we know that  ddx∫f(x)g(x)H(t)dt=[H(g(x)g'(x))-H(f(x)f'(x))] we have ∫xsin(x)t2+1dt…

Q: 20.1 please provide all necessary solutions and explanations.

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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: dy dx sin (a+y) (a is not multiple of x ) sina

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