III. EVALUATE THE FF. ITERA •rU/2 ptan y sec y 1. . x' cos ydxdy Jo . cosy sin2x dy dx xp, •3n /2 pn /2 CC ye* dx dy

Q: 1- Calculate the value of y if: a-y= sin "(0.25) + sinh (2). b- y= sinh (15)+cosh"(31)

A: Note: According to our guideline, we will answer one question. As the exact one is not specified.…

Q: 7. Find dy dx (a) y = (x* + 5x) cos 5x, %3D

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Q: Given: [ Scos(cos2x) sin2x dx Find: du O 2cos2x dx O -2sin2x dx -2cos2x dx O 2sin2x dx O O

A: ∫coscos2xsin2xdxLet u=cos2x.So,     du=-2 sin(2x) dx

Q: 1. Given y= [In(3x² +8)] dy find tan(6x) dx

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Q: 4X dy 2siny ?) S dy sinzx e 3) S sin? dx

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Q: Determine the solution to this DE: Cosx dy +(y- cos"x)dn = 0 cos? x Idx = 0

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Q: 7 6.) Let Y 4(cos' (3x+3)> ニ Find dy dx

A: The given function is y=4cos73x+3. Obtain the derivative as follows.

Q: Given dy find 36 Cos 6x y' dx sin 6x + c 6 sin 6x + c O-6 sin 6x O-36 sin 6x

A: here option a is true.

Q: If y = cos? x – sin? x, what is ? dx dy dy = 2(cos x – sin x) dx dx Option 1 Option 4 dy dy -2(cosx…

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Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: The result of dy/dx for the following function is COS X y = 1+sin x

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Q: The general solution of the D.E. dy/dx + y cotx = 1 is a. y -cotx + c sin x b. y = -tanx + C CSC X…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 4) Find when y? - x2 + cos(x + y) = 0 %3D dx

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Q: 4 Find dy/dx for: y = sec?x- tan²x b- y = sec -x) C- y = sin(tan(3x))

A: It is asked to differentiate the following functions with respect to x: a) y=sec2x-tan2x b)…

Q: du = 3 and dx dy = cos u, find the du dy Given y = sin(3x – 2). If dx 3 cos(2x) 3 cos(3x) 3 cos(3x –…

A: Topic:- derivatives

Q: 1. Evaluate x + x? (y) dy dx. COS

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Q: 14. Solve the equation d?x dx dt +2x sin 3 dr? dx given that at t= 0, x = 0 and %3D dt ment

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Q: 4. Find d2y/dx? for the following functions: a) y = sin x2 cos 2x b) y = cos (sec? 3x)

A: Given that  a)y=sinx2cos2x b)y=cos4sec23x find d2ydx2

Q: help!

A: Refer to the question, we need to sketch the provided function.

Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: Given 5y + cos(3y) = x³ Implicitly find dx Select one: 3x Sy²+sin 3y a. 3x O b. 5y²-sin 3y C.…

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Q: BERNOULL니 dx -X = x siny dy ANSWER; hus -) § losy + Ce) X= -

A: dxdy-x=x3/2sinyx-3/2dxdy-x-1/2=siny                        1 Substituting x-1/2=v…

Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

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Q: ad boda noY BAJUM 7. Find dy/de. dimil nom y = sin [cos(tan 0)]

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Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

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Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: Given dy find y 6 cos 6x dx O sin 6x + c O 6 sin 6x +c O-6 sin 6x 0-36 sin 6x

A: Given problem is :

Q: 5. Evaluate r'sin(y³) dy dx

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Q: 1- Calculate the value of y if: a- y= sin (0.25) + sinh (2). b- y= sinh (15)+cosh (31)

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

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x d'y dx? 1-cos4x 6. if y = 1+cos4x du

A: Topic:- derivatives

Q: -T/6 T So Soo S xy sin(yz) dx dz dy.

A:

Q: 7. y" + y = 3 sin(2r) +t cos(2t)

A: The general solution of an ordinary differential equation of the form;…

Q: given dy=x+coS X find yuhere y( -1.

A: Using variable separable.

Q: implicitly, if e*(e» – 1) + sin(2x + 5y) = In(v7) – · cot(2x) 8. Find %3D y+2

A: Given,

Q: dy cosh x dx + (sinh x)y = e-x

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: a) cos(xy)=2y, find y' DI y = cot-1 1+x 1-x

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Q: S' SE x² cos(xy)dxdy

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Q: dy 4)y = sin-1) veriliyor. i bulunuz ve sadeleştiriniz. dx

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Q: cos(xy) + sin(x/y) = 2y find dy/dx at point (pi,1)

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Q: 3. Find d, where ; a) cos(xy)- (x+y) (x+ =2 + e

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: dy If x = t? cos? 3t y = 3 sin 3t find dx

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Q: (3e + 10 cos(x)) dx ntegral =

A: Integration problem....