Given x = sin3t, y = -cos3t, then find at t =. %3D dx а. 1 b. 3 с. О d. 2

Q: c) dx E (sin cos) dt

A: We find ddx ∫xπ/2   sint2   cost3 dt

Q: Given y = xva² – x² + a² sin¬1 (A. dx

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Q: dy If x=5+cos20 and y=3- sin20 , what is ? dx

A: The solution for the above question is as shown below.

Q: Given æ = 11t – 10 and y = 121 sin t dy (i) dx dy (ii) dx? ||

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Q: -y = tanh" (cos e* ) ||

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Q: solve D.E. by using homo. xsin-- ycos-) dx + xcos-dy = o

A: put y=vx dydx=v+xdvdx differential form  v+xdvdx=vxcosv-xsinvxcosv take x common and split the…

Q: Given that y = sin (t) and x cos²(4t*), hence find dx dy

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

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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: Which of the following is equal to J: x2 dx ? A. sin-1 (t) + € B. sin- (t) + € Option 1 O Option 2…

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Q: Se Ce cos (sin '(x)) COs (sin

A: We need to find the antiderivative of ∫ecossin-1xdv

Q: tanr sec r dx 3

A: Here we will find the antidarive.

Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: Consider solving dx using a suitable trigonometric substitution. After performing substitution with…

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Q: a) Given that y= sinh'(cos(x)), provide detailed derivation to obtain the expression of dx

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Q: If y = sin?t+ tant, x=- In(- cost) - e sinr, find the value of y' when t==. 4 6 A 2 2 2/3 В 2-Vze 2…

A: Use dydx=dydtdxdt to simplify.

Q: TT/2 S,"/e cos?x.sint x dx in tegralinin bulunvz sonucunu

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Q: S sin*xcos?x dx

A: The given integral is ∫sin4xcos2xdx. use the identities:sinxcosx=sin2x2sin2x=1-cos2x2 The integral…

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: VE-1 x= sec?t b) Find for y = dx sint

A: y=t-1sintDifferentiate w.r.t 't'dydt=sint·12t-1-t-1…

Q: Find L-1 () and L(t cos(3t)). s+7,

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Q: Differentiate: y = cos(5 e* ) e11 COS

A: Ans is. option a)

Q: Find dy/dx for the given value of x y = tan-(In x) ; x= 1/e A. e В. е C. e D. Е. None of the above

A: To evaluate the derivative of the given function, apply the following formulas.

Q: Solve the di fferential equation (e'+1) cosx dx+e'sinx dy=0.

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Q: 4. Find d2y/dx? for the following functions: a) y = sin x2 cos 2x b) y = cos (sec? 3x)

A: Given that  a)y=sinx2cos2x b)y=cos4sec23x find d2ydx2

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: dy Find dx 1/4 | sin (?) dt y =

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Q: Calculate L{e-# cos(2t – r)}

A: We have to calculate : Le-2tcos(2t-π) First we will calculate , Lcos(2t-π)…

Q: If we solve the DE y dx + 2 x dy 0 alter converting it to Exad using an

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Q: Given x = 11t – 46 and y = 121 sin t dy dx dy dx? || ||

A: We have to find out the derivative and second derivative of given function

Q: 6 3 oy sin (a? + 3²) dædy Find

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Q: i?? cos(2t) dt csc(10t3)

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Q: The appropriate change of variables for the dx is Vx²-4 x=2 cosØ O x=2 sec Ø O x=2tan Ø O x=2 sineØ

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

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Q: Given: X = 4 cos 20 and y = 2 sin 20 What is the value of d y dx? in terms of

A: We have to solve

Q: Find dx implicitly, if e*(e♥ – 1) + sin(2x+ 5y) = In(v7) – dy 5 ·cot(2x - y+2

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Q: The general solution of the DE dx dy = cos?y is

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Q: implicitly, if e*(e» – 1) + sin(2x + 5y) = In(v7) – · cot(2x) 8. Find %3D y+2

A: Given,

Q: Find the given 5x? cos 2x dx. Using this: "uv – f v du"

A: NOTE: Refresh your page if you can't see any equations. . use integration by parts take

Q: d dx et ex sin x + e* cos x

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Q: (ei-e) dx +x cosh udu = 0 when x = 0; u = 0 1. %3D

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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: Solve the di fferential equation (e+1) cosx dx+e'sinx dy=0.

A: Given differential equation is : ey+1cosx dx+ey sinx dy=0 To solve the given differential equation.

Q: If Xy +y'=1, find at the point Co,-1) 4P dx 2 5- the value of

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Q: Given x = sin4t, y = -cos4t, then find at %3D t = 16 dx О a.3 O b. 2 O c.0 O d. 1

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Q: (b) If y = sin (m sinhx), find the value of (yn)o ·

A: Given   it has to find nth derivative at .

Q: Given that 1 -dr+ 1 - dx = ln a, find the exact value of a. V16+9x? V9+4x?

A: given: ∫01116+9x2dx+∫0219+4x2dx=lna we have to find the exact value of a.

Q: Find the general solution to the following equations: dy 2+ tan y dx

A: The given is the differential equation which can be solved as shown in step 2.

Q: For Cos(2) dx find Ty, My and S,

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