dz If 7 = y cos(x), x = s't and y = s²t³, then dt O a) –2s³ ty² sin(x)+ 6s²t²y cos(x) | O b) –2s° ty² sin(x) O 0)25° ty? sin(x) + 6s²t²y cos(x) d) None of these II

Q: Find y" if y= -4 cos x OA. y" 4 cos x

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

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Q: Solve: (2y cos x + sin* x) da 4 = sin x dy O y csc x + cos ¤ = O y csc x – cos a = C O y csc? x +…

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Q: | cos 3xdx=

A: The given integral is ∫cos3x dx. Let u=3x. Then du=3 dx.

Q: L' (s²+4)(s²+9) 3 f cos(2a) sin[3(t – æ)]dx O b) cos(2t) sin(3t) c) None of these 1 * Só cos (2a)…

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Q: sin adx =? O A. - cos r + 2 Cos cos z | +e 4. O B.-z+2-증 O C. - cos x +2 cos I +C COS D. cos x cos 2…

A: Given: I=∫sin5xdx We know that sin2x=1-cos2x                                              ..1 So, by…

Q: The function y = 4e3x sin x is a solution of dy = 3y + 4e3x cos x dx A) True B) False

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Q: dy If y= sin(sin x), then dx o cos x cos(sin x) o cos(sin x) O cos 3x cos-(sin x)

A: Solve the following

Q: er +6 近 。 Oe) sin(2a) Od) cos(2x) T SOƆ 7 5 Ob cos(x²) + 2x (,r)so) (e O ap UIS .2 hip If y =…

A: Topic :- Derivative Correct option = C

Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

A:

Q: Yp = A1 cos V2t + A2 sin V 2t Which of the following is Yp'? sin v2t A1 V2 Cos /2t A2 V2 O V2A1 sin…

A: Please see the explanation below

Q: 8. S 3tan 3z r sec? 32 da

A: As per the guidelines I can solve only first question

Q: de 6) S 7) S(1 – sin? 3t) cos 3t dt 8) ſ tan (5x) sec?(5x) dx cos? e

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Q: 13. Differentiate 1 3 y = 2x2 + 6x3 – 2x2 а. 2 6 b. у 3 —t 4 3 x2 3 x4 x2 'x3 y = sin³ [cos(tan(3x –…

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Q: Consider the functions below. F(x) = f(t) dt V2 + ut f(t) = 1 du u Find F"(2).

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Q: y = cosx sinx

A: Given query is to the derivative of the expression.

Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

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Q: 2) Sx sin(2x?) dx 3) S cos?(2y) sin(2y) dy 4) f sec3 x tanx dx

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Q: dy If y = cos (sin2x), then - 6 cos² (sin 2x) sin (sin 2x) cos(2x) dx True O False

A: Given: The function is  y=cos3(sin 2x)

Q: Fill in the blanks: 1. If tan z = 2.5 then tan(-x) = 2. If sin x = 0.1 then sin(-x) = 3. If cos x =…

A: 1. tanx = 2.52. sinx = 0.13. cosx = 0.8 To determine: The values of tan-x, sin-x and cos-x for (1),…

Q: Find y" if y = 5x sin x. O A. y" =5 cos x- 10x sin x O B. y"= - 5x sin x OC. y"= - 10 cos x+ 5x sin…

A: Solution: The objective is to find the double derivative of the given function

Q: 3. sin(x +y) + sin(x - y) = 2 sin x cos y

A: The given identity

Q: 26. Show that |sin z sinh2 y + sin2 x.

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Q: M tan? x dx

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