9. A particular solution of y" +9y = 3 sec 3x is (a) z = cos 3x ln | sec 3x + x (b) zcos 3x ln | sec 3x + x sin 3x -3 sin 3x ln | sec 3x + tan 3x| (c) z = (d) z = (e) None of the above. sin 3x ln | sec 3x + tan 3x + x cos 3x

Q: a3 2- Find the third derivative for = sin(÷) for f(x, y) ax3 -2sin?cos()+2 sin A:- ) sin()+3cos )…

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Q: 1. f(t) = cos*t – sin*t 5. f(x) = tan 2x 1-cot 2x 2. y= sec20 – tan²0 3. f(x) = sin(cos x) %3D 3 4.…

A: Here we have to find derivative of given questions.

Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

Q: Find y'' if y = 6x sin x. A. y' = 6 cos x - 12x sinx B. y'= - 12 cos x + 6x sin x C. y' = 12 cos x -…

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Q: 5. (3x-17) dx / (x² - 6x + 10) 11

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

Q: Find y'' if y=-6 cos x. OA. y' = 6 sin x OB. y' = 6 cos x OC. y'= -6 cos x OD. y'= -6 sin x

A: The function is given byTo determine: The expression of the second derivative of the function.Formul…

Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: 3. sin²xcos³x = cos x(sin²x - 2sin*x+ sinºx)

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 1. If z = sin2+In^, find the value of x- +y X

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Q: Find y'' if y=-8 cos x. OA. y'=8 sin x OB. y'= -8 cos x OC. y'= 8 cos x OD. y'= -8 sin x

A: Explaination of answer is as follows

Q: 10x 19) y Sin'(5x') (ans.: JI-25 x' 20) y= Cot ) (ans.: 1+ x' 6x' 21) y=tan'V4x'- 2 (ans.: (4x'-1…

A: As per guidelines we can only solve first question or first three subparts of the question, I am…

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: e of mwl

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Q: I. Functions and Limits 1) If f(x) = x2 – x + 3, find f(-5y) and f(x³) x2-1 2) lim X-1 2+3x-4 3) lim…

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Q: (c) tan x = 10t' (e) tan 12t-x¹2 (d) 16 sint- cos 17x= cost, = sin 12x.

A: For the derivatives of the given functions dxdt are as follows (d) dxdt=-(sint+16cost)17sin(17x) (e)…

Q: (a) (i) Use the substitution sin(u) = x + 3 to show that dx 12x + 7 -1 (x+3) V-2x² – 12x+7+c. sin -…

A: As per company guideline we are supposed to answer only one question with maximum 3 sub parts at a…

Q: 8. y"+y = 3 cos 2.xr,

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Q: S(csc x cot x + 7x°)dx - sin x + x' +c x7 Csc x + x' + c sec x + x' +c csc x + x' +c -

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Q: No. 11

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Q: 1. y' = 2. y'= 1 cos x cos y 3. y' = 3 cos x cos y 4. y' = cos x sin y = 2 cos x + sin y

A: 1.2.

Q: If f(x) = 5x(sin x + cos x), what is f'(x)? O 5 (sin(x) + cos(x)) -5x (cos(x) - sin(x)) No correct…

A: Derivative of product: ddxuv=udvdx+vdudx

Q: 4) If y = 2√x - 2 tan-¹ √x, then y y' = -1 1+x²

A: Given :y=2x-2tan-1x

Q: d dx [ 3+√√f(sin( sin(x)) cos(x) f' (sin(x)) 2√f(sin(x))

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Q: Find y'' if y = 2x sin x. O O O A. y'' = 4 cos x - 2x sin x B. y'' = - 2x sin x OC. y'= - 4 cos x +…

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Q: 5. (a) C Evaluate sinxcos³ xdx 1 1 sin³ x+-sin³ x+C 3 5 3 sin x sin³ x+C 1 (b) cos³x-cos³x + 1 (d) 3…

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Q: 3 5. y= 23x+1 %3D 2 3x+1

A: Given : y = 323x + 1

Q: 2) x³y? = 2x + 2y3 3) y = sin?(x) – cos³(2x) + 2 www. .

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Q: (2 cos x + 7 sin x) dx

A: Disclaimer:  Since you have asked multiple questions, we will solve the first question for you. If…