Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos (y²)

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

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Q: Sx' cos(x4) dx = o 1 cos(x*) + c 4 - -1 - cos(x*)+ c 4 1 sin(x*) + c 4 -1 sin(x*) + c 4

A: *concept :- let, x^4 = t then integrate the simplified term cos(t).

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

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

Q: What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

Q: |2tan x In (cos x) dx=

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Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

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Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: SOLVE THE EQUATIONS

A: Given:

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: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

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: 3+2cosx dx is equal to (2+3cosx) sin x 2 cosx 2+3cos x) 2+3sin x 2 cos x 2 sin x (d) 2+3cosx 2+3sin…

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Q: [ 2x sin (4x)dx O =cos (4x) + C -x² 4 2 sin (4x) + 8x cos (4x) + C sin (4x) – x cos (4x) + C ○중cos…

A: Integration by parts

Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

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: 2. [ * xkbr cos*x- sin 3(sin y- cos y)° dv 10. cos y

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Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

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Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sin-1 (xyz)

A: Given that f(x,y,z)=sin-1(xyz)

Q: 1. y = In (3 – 4 cos x) + (4x – 5)5 2. y = x² tan x 3. y = x5 sin2x cos 4x %3D

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

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Q: 2 sin 2x dx Tcost x + 4 cos² x – 2

A: We will answer the first question since exact one was not specified. Please resubmit the question…

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: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 3x cos 8x dx e3x e3x A) [8 sin 8x - 3 cos 8x] + C B) [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x + 3…

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

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

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: 1. S(esin x cos x - acos 2x sin 2x)dx

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: V3 with 0 < x < 2n. 2 cos 2x cos x – sin 2x sin x - -

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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: Show that sin(x^2) ≤ sin x for 0 ≤ x ≤ 1. Deduce that sin(x^2) dx ≤√2/2 on the invterval [0, π/4]

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Q: 19. i) Differentiate sinx with respect to x from first principle 1+3x dy ii) Find, dx when a) y (x…

A: Part i,Given,          fx=sinx

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

A: Topic:- derivatives

Q: Differentiate y= sin'x- cos³x CO A. 3sin x cos x (sinx - cos x) COS B 3sio x cos x (sinx + cos x) C.…

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Q: 11. y = x² sin x + 2x cos x – 2 sin x 12. y = x² cos x 2x sin x – 2 cos x - -

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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: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

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: 4 sin' 2x cos 4x dx 4.

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Q: ind the equation of the line that is tangent to y = 2x + sin x + cos x at x = 0.

A: NOTE: Refresh your page if you can't see any equations. . take x=0 the point on the graph is

Q: 4. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

A: 4) Given:            ∫3sin2t-3cos5tdt       =∫3sin2t dt-∫3cos5t dt taking constant out…

Q: (0)3-3x+2 sinh' (In x) cosh (In x) (E) sin(2x)dx dx N

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Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

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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: when

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Q: 17. Evaluate f-3x cos 2x dx a. --cos 2x - 3xsin 2x + C b. -cos 2x -sin 2x + C C. -cos 2x -³x sin 3x…

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