What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point %3| 2 y = x + y = 0 y = x 2 ||

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

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Q: find dy/dx.1. y = -10x + 3 cos x            2. y = 3/x + 5 sin x3. y = x2 cos x…

A: Given the functions :- 1.  y = -10x + 3 cos x Differentiating with respect to x dydx =…

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: The solution of following Differential Equation dy sec²y+x tan y = x³ , is %3D dx

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Q: 2. Consider y = cos(2x). 2.1. Find Y dx 2.2. Determine an equation for the tangent line at x 0.

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Q: 1- Find the equation of the tangent to the curve y = 2 sin x+ cos2x at the point x = n. 2- Find the…

A: Solution:

Q: ( 2x – sin y) dx – (x cos y) dy = 0 -

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Q: 3. Find y' for y= cos(sin² x) 4. If x=y√/1-y², find y dx

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Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

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: This differential equation is linear. What is the Q(x)? * Cosx dy t (y- cosx )dn = 0

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Q: Solve exact equation 2x -)dx + (2x cos(2xy) + 8e²")dy = 0 x² + 1 (2y cos(2ry) + with initial…

A: We will solve the problem.

Q: 4. Integrate COs x dx

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Q: find the derivative (dy/dx) of the given function:  1. y= e^X sin X 2. y= (cos x)^9 3. 1/ ln(X)  4.…

A: Given,

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

A: to find the slope differentiate  the equation with respect to x .

Q: 2. cos x cos y dy-sin x siny dx = x² cos x sin y dx

A: The given equation is: cos x cos y dy-sin x sin y dx=x2cos x sin y dx Dividing it by cos x cos y we…

Q: dy tan tan x = 0 dx coscos 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 a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: The equation of the tangent to the curve y=4+ sin' x at X=0 is O y = 4 O y = 2 O y = 6 O y = 3

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Let z=sin (y 2- 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: Show that the solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is  1+tan(x+y)/ 2 =…

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

A: Gamma function

Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

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Q: This differential equation is linear. What is the P(x)? * Cosa dy + (y- cos'x')da = 0

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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: x + y sin 2 ) dx x sin 2 dy = 0 -

A: The solution is given in the next step.

Q: 1- S7 cos(y)eSin(y)+9X dydx

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Q: Ssin (2x)cos(2r)dx

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Q: 8/ (e* sin y +3y)dx -(3x-e* sin y)dy = 0

A: Given thta  The differential equation

Q: What is the solution of the equation dey/dx=y/x+tany/x

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Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

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

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Q: 2. Find the length of the curve: y = 2 In (sin (÷x)); -< x

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Q: Explain why the initial Value problem dy/dx=x-cos(y); y(1)=pi has a unique solution. For that…

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Q: Find an equation of the line tangent to graph of y =x2 + sin (Ex) at x=-1. A. 2x - y+2 = 0 B. 2x +…

A: To find the equation of tangent line of the given graph.

Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

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Q: Question 4 Solve y at x=1. dy/dx - 2(x+1)^3 = 4y/(x+1)

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Q: -20 Find dy/dx by implicit differentiation y 20. tan(x – y) 1 + r .2

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Q: Sin (7€) + Cos (SE) 5지

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Q: Dy/dx of tan y=ln (cos2 y/ 1 + sin y)   - x

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

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Q: 2- find dy/dx e2x = sin (x + 4y) 3-find an equation for the line tangent to the graph f(x) = x –…

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Q: (a) f* (1 – cos 3t) sin 3t dt,

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Live of y = e(x+ln x) cive of ƒ(x) = 5x6 – sec jye of y = e(sin x) e(sin x) - sin(e

A: We have to find the derivative of the given function

Q: 4. cos x dy + y(sinx- 1) dx = 0; when x = n, y = -2

A: (4) To find: The solution of differential equation. Given: The differential equation is…

Q: (y cos x + 2xe") dx + (sin x +x²e + 2) dy = 0; when x = 0, y = 0

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Q: 10. Find dy/dx of y= 1/ (tan-1 x)

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