What is the line that corresponds to the phase shift of the function f(x)=tan (π/2 x−3π/2) +4?

Q: The solution of the differential equation tan xdx + tan ydy = 0 is

A: Using variable separable method.

Q: y=cos-1(3x2+1)=arccos(3x2+1)

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Q: 10) 4xy dx - (6x² +y) dy so

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Q: Find the differential of the function. Y = e2x

A: Given function is  y= e2x

Q: Is y'' = sin x a linear differential equation?

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Q: Determine whether the differential equation is exact or not exact. (-4xy sin(x) + 8y cos(x))dx + 8x…

A: Solution:-

Q: Find dy/dx if y= tan-1(x/(1-x))

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Q: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: i) Solve the differential equation dx +tan x tan y = cos x secy.

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Q: dy соmpute dx for implicitly given function cos(xy) + 2y = x³

A: cos(xy)+2y=x3Differentiate with respect to x,-(sin(xy))y+xddx(y)+2ddxy=3x2

Q: Let z= sin (y2 – 4x), Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: Solve the differential equation (2xy - tan⁡ y) dx + (x^2-x sec^2 y) dy = 0.

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Q: The graph of x4 + 2x2y2 + y4 = 9x2 - 9y2 is a lemniscate. Find dy/dx by implicit differentiation.

A: The graph of x4 + 2x2y2 + y4 = 9x2 - 9y2...(1) is a lemniscate. To Find dy/dx by implicit…

Q: Construct an autonomous first-order differential equation dy/dx = f(y) whose phase portrait is…

A: Consider the given figure. From the figure, it can be noted that the critical points are 0 and 2.…

Q: 1. Find the y" of y = (4x - 3x + 1) (5x + 7) 2. Find y" given y = cosx + sin 3x 3. Find all the…

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Q: 1. Find the derivatives of the given functions. a. y= arccos(x b. y = In (arctan x) c. y= csc (2u+1)…

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Q: 2- Find dy/dx for y = In(tan(2x2))

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Q: 5

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Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: Find the derivative of y with respect to x. y= sin -3 O A. XV1-x - 3 O B. 1+x - 3x 3 c. 1-x -3 O D.…

A: Given that: y=sin-11x3

Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: Find dy/dx for y=cos^-1(x^1/2)

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Q: 11. Sketch the phase portrait and bifurcation diagram near = 3.

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Q: Task 2 Verify that the function y(x) = sin(x³) is a solution of the %3D second-order differential…

A: Given  Second order differential equation: y'' - 2/x y' +9x4y=0 To prove : y = sin (x3) is solution…

Q: Find the derivatives of the functions in Exercise y = t tan-1 t - 1/2 ln t

A: To find: The derivative of y=t·tan-1t-12ln t Concept used: Product rule of derivative: uv'=u·v'+v·u'…

Q: 22. Find the required derivatives. a) y = (4x3 - 2x + 1)-2; find y b) x = Vy? + 1;find x"

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

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Q: (y-cos^2 x) dx + cos x dy = 0

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Q: the chain rule - find dy/dx (derivative) of y= (4x11 + sin(5x))1/8

A: We have been given a composite and complex function, and we are required to find its derivative. In…

Q: Find the differential of y² + x = 4.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find dy dx 2. y tan-¹(csch x³)

A: Given y=tan-1 (csch  x3 )

Q: 1. find dy/dx of each equation using implicit differentiation. a. x2 - y2 = 9 b. 3x2 - y3 -3xy = 0

A: As we know that; The Power law; ddxxn=nxn-1 The Product rule; f·g'=f'·g+f·g'   Given: (a). x2-y2=9

Q: Find the function y = f(x) whose graph passes through the point (5π/12,3.5)if dy/dx =cos(2x−π/3).

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Q: Find the second differential of the function y=x2cos2x.

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Q: Find the differential of the function. y=x^4 (sin(8x))

A: topic:-  derivatives

Q: Can you help me with this problem step by step?

A: Given:

Q: Find dx (e3t + 1)dt. -cos(3rx)

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Q: Sketch the phase plane of the differential equation * + 8¢ = 0.

A: Given that x¨+8x˙=0 This can be re written as, x˙=-8x So, the second order is changed to first…

Q: Find dy of the function y = cos2 3X + √√Sin x dx

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Q: Demonstrate that the function f(x)= e^-x sin (x) is a solution for the differential equation f(x) +…

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Q: Find the third order derivative of y = In(cos(2x)). A. y' = -40sec? (2x)tan(2x) B. y' = -80sec?…

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Q: Solve for the differential of y when y- sinax. x= and dx O o o

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Q: Verify that the function y (cos( 6x)) is a solution to the differential equation y = 6 sin(6 9e

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Q: ) Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) = 5sinh(y)

A: We need to find dy/dx.

Q: Find dy/dx by implicit differentiation. tan-1(4x2y) = x + 3xy2 y' =

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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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Q: Find the differential of the function   y = θ3 sin(6θ)

A: Solution :-

Q: Find the slope of the graph of cos(x + y) = 2x at the point ( 0, T1/2 ). Hint: Differentiate…

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