Differentiate y= e*cos (x²): y = A e(cos(x?) – 2xsin(x?)) B -2xe"sin(x?) (c) e*cos(x²) – 2 xsin(x²) D - e*sin(x?)

Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: Evaluate [[ sin(y²)dydx where 2: 0<y<1, 0<x<y°. 0 x b) a-cos¢x)) (1 a) 1-cos(x) 1 - cos(1) c) 2 d)…

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Q: Find integral.

A: Given: Let I=∫2x cos x2 dx To Find: To evaluate the given integration.

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: of (e² 2-X Sin (2y)

A: Given, f= e2-xsin-1(2y) To find, df/dy.

Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: SOLVE THE EQUATIONS

A: Given:

Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

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Q: Consider the following IVP: y +y = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: Find y, of (D² + 1)y = sec x = In |cos x| (cos x) - x sin x В y = x sin x + (cos x) In sec x = x sin…

A: Please see the below picture for detailed solution.

Q: nx and y=cosx from x=- to x=- 4 4

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Q: 1 1 S [ sin(1+ y²)dydx= 1- cosl a. 2 cos 5

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Q: Integral of sin^3 x dx over cos^4 x

A: In this question we have to find the Integration.

Q: y f(x)sin2x + g(x)cos %3D x) =tan3x x)% sin3x %3D - r) =cos3r

A: Differential equation: y''+9y=tan (3x)The auxiliary equation is,m2+9=0m=±3iComplementary function…

Q: 1 Evaluate [ (x³ +cos(3x))dx 2

A: The given integral is ∫x3+12cos3xdx.

Q: Use linear approximation or differentials to approximate cos (1.6)

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Q: - / sin 8x cos 5x dx = 1/6 cos3x + 1/26 cos13x + C ) -1/6 cos3x + 1/26 cos13x + C ) -1/6 cos3x -…

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Q: Suppose that 2x² - y² = t² and x = t cos 0. Find (a). ¹(2), X and 0

A: answer is in next step

Q: establish each identity.

A: Given  The identity is ln sec θ=-ln cos θ

Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

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Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

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Q: One approach to evaluating 2 cos (2x)dx is to first rewrite it as cos(4x) + 1 dx а. cos(2x) – 1 dx…

A: This is the question of integration.

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: (a) Show that cos(x²) > cos x for 0 ;. 1

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Q: 11 Evaluate ff sin(y²)dydx where 2: 0<y <1, 0<x<y°. 0x a) 1-cos(x) b) (-cos(x)) --cos(1) d). cos(1)…

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Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: Find the indefinite integral ∫cos 2x cos 6x dx

A: Given integration as I=∫cos 2x cos 6x dx Since  2cos 2x cos 6x=cos 6x+2x+cos 6x-2x…

Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: Find dy/dx: y = sin (In x²). A 2 cos (In x²) (B) 2 cos (In x²) / x

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Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: 3 2 1. + cos x) dx x3

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: find | cos*x dx 1 1 1 А) — — х —- sin2x + —x + — sin4x + c 4 1 B) =-x +- sin2x + X 4 1 8 1 x + sin4x…

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Q: 2- Find of y = dy dx y %3D /cos-1(In (xy))

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Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: 4. y = tan(x+ a), 5. y = Aex + Be2x, 6. y = A sin 3x + B cos 3x, ,where A and B are arbitrary…

A: According to bartleby guidelines when student ask multiple subpart question then expert must have to…

Q: Find and simplify the result whenever possible dx 1. y=x+sin2x 1. y = 4 1 sin' 5x 3 2. y sin5x - 3.…

A: Solving for the number 4:                                          4) y=3xcos(x3)-9 sin(x3)   To…

Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: 2 Given that: J2(x)=-, cos.x + sinx find J(x)

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Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

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Q: Differentiate y= e*cos (x2): y' = A -e*sin(x²) e(cos(x²) – 2 xsin(x²)) e*cos(x?) – 2 xsin(x²) D -2…

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: v² operates on sin(-3x) + cos(3y)

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

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