Find d?y if y = t sin? 2t and x = cos? t dx2

Q: 2 X(+) = SIN'セ y (t) = Cos?t 9) IF dy FIND %3D

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Q: find the value of the constants a, b S"L cos(x + 2y + 3z)dzdydx = TT a

A: Triple integral

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: If z = x?y + 3xy, where x = sin 2t and y = cos t, find dzidt when t = 0.

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Q: -/- I = х cos bx dx, for b > 0

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

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

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Q: L(S,(3r² – cos t)' dt)

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Q: (b) dx cos(t) a

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Q: T/2 sin? x cos x dx 50.

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Q: d²y c. Find dx? if y= sin’0 , x= cos’e

A: We have y=sin3θ    and x=cos2θ We need to find d2ydx2 Now,  dydθ=3 sin2θ ddθsinθ=3 sin2θ cosθ dxdθ=2…

Q: 5 sin?(t) cos“(t) dt

A: ∫0π5 sin2t cos4t  dt=5∫0πsin2t. cos2t .cos2t dt=5∫0π sin2t ×1sin2t cos2t dt=5∫0πcos2t…

Q: d. 3) [cos πx]4 %3D dx

A: 3) To find the derivative

Q: Given: x = 0 – sin 0; y = 1– cos 0 d'y Find: dx?

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Q: Given: x = 0 – sin 0; y= 1 – cos 0 d'y Find: da?

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Q: Given z = 2 cos t + 26 and y = 5 sin? t dz dy dy dz

A: Derivative of function in parametric form

Q: T/2 S sin? x cos5 x dx

A: Topic = Integration

Q: dy b) Solve cos?x+y = tan x dx.

A: In this question we have to solve the differential equation.

Q: T/41 – cos X dx sin?x Jπ/6

A: The given integration is ∫π6π41-cosxsin2xdx

Q: Given æ = 2 cos t + 12 and y = 6 sin? t dx (i) dt dy (ii) dt dy (iii) dx || ||

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Q: dy The general solution of the DE cos?y is dx A y=tanx + C y=tan-(x) + C у-cos"(x) + с D y= sec?x +…

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Q: y(1) = yo + A cos(@t + p)

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Q: L[ cos? (t) – sin²(t)] = ? %3D 2 S s2 -4 s² +4 2 s2-4 s2+4 O c

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Q: T/2 dx L a+ sin? x' ļal > 1,

A: As too many questions are given, So I will solve only the first question. Consider, ∫0π2dxa2+sin2x…

Q: d²y Answer: 1 . If x = t + cos t, y = sin t, find dx2 dx2 (1-sin t)

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Q: T/4 sin? - cos? x dx COs x T/4

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Q: d?y 1ay +x² cosx +x² cos.x x( dx x> 0. dx?

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

A: We will solve the problem

Q: Given z = 9t - 36 and y = 81 sin t dy (i) 9*cos(t) dx dy (ii) da? -9*sin(t)

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Q: Given x = 2 cos 2t and y = 5 sin t. Find when t = dx

A: Given:

Q: 2) y = e°(sin e + cos e)

A: I understand that we need to find the derivative of this function as nothing is mentioned

Q: -2t L{e cos? 21

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Q: A شعبة Given x2 + y? + z? = sin (yz) find dz/dx %3D

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Q: Given x2 + y? + z? = sin (yz) find dz/dx

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Q: d?y Suppose that y = sin? t and x = cos t. Then dx2 x=3 1 2 -2

A: Given: y=sin2t, x=cost

Q: 1 dx cos? x (m) klom

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Q: dx (b) | sin x· cos? x

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Q: 3) I = dx 4) 1 = S cos?x dx

A: Given that

Q: The general solution of the DE dx = cos?y is A y= sec?x В y=tanx + C y=tan-1(x) + c y= cos os-(x) +…

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Q: d’y Find dx? 2 2 1. y = sin 2x +cos x

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Q: Given a = 2 cos t + 26 and y = 5 sin? t dz dt dy dt ||

A: Simply take the derivative using basic concept of derivative.

Q: Find (d^(2)y)/dx^2 if y=sin(x)cos(x)

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Q: Find the solution of sin 3ædx + 2ycos³3xdy = 0 O y? = sec 3xtan 3x + C O y? = -sec 3ætan 3x + C O y?…

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Q: 3 y = sin?x? ; find dy 13D Xp

A: We will use simple differentiation rules to solve this question.

Q: d’y If y= cos 2x, then at dx? x = 0

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Q: 2. Given xy? =Sinlyz find dź/dk

A: We are given: x2+y2+z2=sinyz Differentiating both sides with respect to x, we have…

Q: If L(ešt + cos(3t)) = As²+Bs+C (s–5)(s²+9) the value of C is

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Q: T/2 (cos(7x) + T) dx? 0.

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Q: dx b) sin x· cos? x

A: let's find integral

Q: dw Given w = 2ye? sin(xz), find : dw and dz dy

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