If r(0) = tan(sin 0), then r'(0) is:

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: s sin(3x) + cos(5x) – sin sin)ax |dx

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Q: Find the solution of the equation = e Cos y which tends to zero as x → 0o and has the value cos y…

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Q: Solve the DE: (cos y- cos x)y' +cos y sin 2x=0

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Q: {e* cos x , e* sin vx}

A: Given that: {excosx, exsinx}

Q: Find the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in in the…

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Q: -을 x e [T, 3 J Sinx =

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Q: Find the solution of the equation Cos y which tends to zero as x → 0o and has the value cos y when…

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Q: Solve for f(x) the ir f f(x) cos px 8 sin² t

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Q: Find the solution of the equation = e cos y which tends to zero as x → 0o and has the value cos y…

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Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

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Q: Show that both y = sin x and y = cos x satisfy y" = -y.

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Q: z = y sin(2x) + (1 + x²)e* + cos x tan¬(y* + 1) In(y6 + 137)

A: ∂z∂x=∂∂xysin2x+1+x2ex+cosxtan-1y4+1lny6+137=∂∂xysin2x+∂∂x1+x2ex+∂∂xcosxtan-1y4+1lny6+137=2ycos2x+1+x…

Q: Find the slope of the curve 2xy = In(e2*) sin(x) at the point (2,2)

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Q: Let f(x)= 9 sin x/ 2 sin x + 4 cos x Then f'(x)= The equation of the tangent line to y=f(x) at a =…

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Q: (c) Show that the function z -- eX sin yt ey cos

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Q: 4. J (cos x – sin x)²dx

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Q: 3. Explain graphically: cos x dx = 0.

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Q: (d) ƒ sin(1 – x)(2 – cos(1 – x))ª dx

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Q: Differentiate y = e*cos x У'3

A: To find the derivative of the function which is exponential in nature

Q: At what points the curve x = 2a(cos(t))-a(cos(2t)), y = 2 a(sin(t))-a(sin(2t)) has vertical and…

A: Given: The curve equations are shown below. x=2acost-acos2ty=2asint-asin2t Calculation:…

Q: Find the solution of the equation = e cos y which tends to zero as x → 0o and has the value cos y…

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Q: x4 1 If u = tan(- + y° x² – y² - then show that ди du + Y- ду X - = sin2u dx

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Q: dx. (a) [ cosʻ x+4 sin x (i) Evaluate Using the substitution ttanx

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Q: Differentiate. y = e cos x + Cos( ex)

A: Given- y=ecosx+cosex To find- The value of the derivative of the above function. Formula used-…

Q: Se2* (sin x + cos x)dx

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: (a) Find dy for dx = In (3x – 2) (tan 2x) -

A: Explanation of the solution is given below..

Q: (d) sin (x )+tan dx – In +y = 0

A: We have to solve given problem:

Q: What is if z = x'y+ sin(xy²)?

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Q: Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x)

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

Q: x³ + y³ + 3 x² siny tan z = 5 az dz and əx Find ду

A: Given,          x3+y3+3x2sinytanz=5

Q: satisfied

A: We will solve the problem.

Q: Suppose x and y are functions of a third variable t. If sin-(x) + cos°(y) = = and dr dy what is the…

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Q: 1 dx 3 sin x+4 cos x+3

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Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: 11. sin(x) + cos(y) = ey

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Q: Find the solution of the equation +. cos y which tends to zero as x → 0o and has the value cos y…

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Q: 1 dx J 3 sin x+4 cos x+3

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Q: S cos(e) In (sin(0))d0

A: We take the help of integration by parts in solving this problem

Q: 16. S(3 sin 0 + 5 cos 0)d0

A: A detailed solution is given below     ( As per our guidelines, i have to answer only 1st question…

Q: We know that x =r cos 0 and y =r sin 0, then find the derivative af /ər if 1 f = x2 + y2

A: Given f = 1x2+y2  and x = r cosθy = r sinθ Thus f = 1r cosθ2+r sinθ2= 1r2 cos2θ+r2 sin2θ=…

Q: Let f(x,y) = tan 1(sinh (y) + 2020 cos - 'y) + 4xy Calculate

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Q: X cos (3x) dx,

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Q: Find the solution of the equation Cos y which tends to zero as x 0o and has the value cos y when…

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Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

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