d²y dy and - dx B) Find if x = sin? 3z and y = tan 3z dx2

Q: Find ди ds if w = sin(xyz), x = 1 - 3t, y=e¹-t, and z = 4t, find o

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Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: The dv of sin-lx dx is dx. A) True B) False

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Q: 3) eYsinx dx = cos?x dy 4) y' + (÷) y = xy?

A: First question we can easily solve using veriable separable method. Second question we can use from…

Q: dy 7. dx cos(x + y), when x = 0,y = 4

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Q: dy If dx = COS s 2x, then what is y?

A: The derivative is given by dydx = cos2x                         ........(1)

Q: F ind So S. eu dy dx.

A: Use the concept of reversing the order of integration. While integrating with respect to one…

Q: (a) If y = tan x, prove that y = 2(y2 + 1)(3y2 + 1). (b) Find y' for y cos(sin?x). %3D %3D dy (c) If…

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Q: d Q 3. Prove that tanx dx sec?x. =

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Q: dy If x = sin? (u) and y = cos2(u), then %3D dx

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Q: 2 sin(t) s(t) = et

A: Part (a) The displacement of the object is, s(t)=2sintet Integrate the expression with respect to t…

Q: Given dy find 36 Cos 6x y' dx sin 6x + c 6 sin 6x + c O-6 sin 6x O-36 sin 6x

A: here option a is true.

Q: dy d²y B) Find if x = sin² 3z and y = tan 3z and dx dx2

A: We differentiate the function.

Q: 4- Find dy/dx for: a- y = sec?x – tan?x b- y = sec³ ( – x) %3D c- y = sin(tan(3x)) d- y = /1+ sin³…

A: NOTE- Since questions 1, 2, 3, 5 and 6 are incomplete, so solving question 4 only. Please submit the…

Q: cos ax -dx = re¯ª,a>0. .2

A: With the help of Residue we can prove given result:

Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

Q: where yco,t) = y (5,t) = = 2Jx2 and y cx, o) y (X,o) = 10 sin 4T X

A: We solve the differential equation by the method of saperation of variable. In this method we…

Q: d²y dy and dx Find if x = sin 3z and y = tan23z dx2

A: It can be observed that both the variables x and y are the functions of  z, therefore to find the…

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

A: Introduction :

Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

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Q: dy Find for y = sin (2x +3) da %3D Ans=

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Q: 4Find dy/dx for: y = sec?x - tan?x b- y = sec -x) C- y = sin(tan(3x))

A: Since, you have posted multiple questions and the questions marked by you has multiple sub parts ,…

Q: find dy Say y=3 Sin 8)

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Q: rcosA 2. r sin 0 dz dr de

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Q: d'y Given that x= sec 0 and y= 2 tan 0. Find dx?

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Q: dy Let y=e* sin 3x. Show that 3e-2* cos 3x - 2y. dx -2x d'y = -13y-4- dr Hence show that dx

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Q: If y = sin(msinx) then show that (1– x)' y, – xy, + m² y =0.

A: Given: Given y=sinmsin-1x We want to show that 1-x2y2-xy1+m2y=0

Q: If x = t +cos t, y= sin t, find d^2/dx^2

A: Given that      x=t+cost , y=sint  Here we have to find d2y/dx2 .

Q: For S* sin x dx, what is dv? sin x dx OA 2x dx - cos x+ 2x sin x+2 cosx+C O.

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Q: dy/dx = cos3x/sin2y. Given y=pie/2 when x=pie

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Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

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Q: dy Find if y = 4 sin?(3x) dx

A: Here we have to find the derivative of function y which is given as above. Here I am attaching a…

Q: (b) Find, where y= cos ecx- dx -4x+7

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Q: dy 7. Find ,y = cos³xsinx? dx

A: Given: y=cos3xsinx2 Formula used: Product rule of derivative: ddxf×g=dfdx×g+dgdx×f Power rule of…

Q: 3- dx for y x sinx is equal to: a)2x cosx b) 2x sinx + cosx 2x c)x cosx+ sinx 2x

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Q: if z=ex( x cos y-y sin y ), show that  ∂2z/∂x2+∂2z/∂y2=0.

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Q: If y = (sin¬1 x)², show that dy (1 – x²) da? dy = 2. dr

A: y=(sin-1x)2 we have to show  (1-x2)d2ydx2-xdydx=2

Q: dy is: If y = tan(47x²) then dx

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Q: ) Solve to find if y = sinvt – t, and t = cos (2x) – secx dx

A: Given: y=sint-tt=cos(2x)-secx To find: dydx

Q: In Va? + b² dx In x arc tan- Jo (x + a)² + b² where a and b are real.

A: We will prove the given identity by solving the integral using appropriate substitution.

Q: cos(xy) + sin(x/y) = 2y find dy/dx at point (pi,1)

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Q: dy =1+ sec' y dx If sin y = 2 sin x show that

A: Given  siny=2sinx

Q: If x=sin8,y=0 ,y=cosp0,Prove that (1-x') y,-xy,+p°y=0 where y2 d'y dy and y,- dx? dx

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Q: 3e7" sin(2y) 3e7 sin(2y) dy

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Q: sin?x d Prove that 2sinx dx \(1+cosx)² (1+cosx)²

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Q: Determine whether the statement is true or false. 4 '1 (x2 + Vy) sin (x?y²) dx dy < 9 1

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Q: dy 7. dx = cos(x + y), when x = 0,y == 4

A: Differential equations, with substitution method and separation of variables

Q: C. Given that y = e* sin x, show that d?y +2y 0

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