Question 4 (cos(2x) – sin(2x) cos( 2x )) dx=- cos(x) – sin(x) -F(x) +C. For -C. What is F (x)? 3 A (csc(x) – sec(x))3 ® sin(x) + cos°(#) + cos(+) + in°C«) B) -cos (x)+ cos 3 -cos³ =sin³ (x) 3 2 2 sin (x) - cos? (x) – cos(x) + -sin³(x) 3 3 1 D (sin(x) – cos(x)) -3 - cos

Q: Find h'(x) if h (x) (2 csc x) (5 sin x - 3x). O-2 cot2 x (5 sin x - 3x) O2 cotx (5 cotx - csc x) -2…

A: Givenhx=2cscx5sinx-3x We know that cscx=1sinx We know that dcscxdx=-cscx.cotx Product rule for…

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A: The given expression is: cos π3-x Note that: cos θ=sin π2-θ

Q: Find the value →21. csc (sec- 2) + cos (tan¬1 (– V3))

A:

Q: x2 In solving for the antiderivative of f(x) = (9 – x2)32 using trigonometric substitution, Jf(x)dx…

A:

Q: If f(x) = = sin (3 – x), then f'(0) O 6 sin 3 cos 3 O 6 cos 3 O -2 sin 3 cos 3 O -2 cos 3 -2 cos O 2…

A: f(x)=sin2(3-x)

Q: If f(x) = cos x + sin x, what is f"" (x)? 46 f""(x) = sinx- cos x f"" (x) = sin x + cos x o f(x) =…

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

Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

A: Given

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A: See the details solution in below

Q: Let f(x) = 9 cos(cos x) f'(x) =

A: The given function is fx=-9coscosx. We know that if fx is a function then f'x if the derivative of…

Q: f"(x) = 5ex - 8 sin(x), (0) = 3, f(x) = 5+ 5e + 5e* + 8 sin(x) – 1

A:

Q: 3 sin a If f(x) –, then 2+ cos x 3+ 6 cos(x) (2+ cos (z))² f'(x) = f'(5) =

A: For part (b) just put 5 in place of x in the expression of part (a).

Q: Let `f(x)= (9 sin x)/(2 sin x + 4 cos x)`. (9 cos x) (2 sin x + cos x) – (9 sin x ) ( 2cox – 4 sin…

A: Given f(x)=9sinx(2sinx+4cosx). The objective is to find f'x and equation of tangent line at π2.

Q: f(x)= 2 sin x / 2 + cos x Find f’(x)= Simplify your answer. (Quotient Rule) Please explain it step…

A: Given query is to find the derivative of the function.

Q: (a) y = In(sec²x) (b) y ecos + cos(e) x² −1+2 (c) y = x (d) y = sin² (e) y = (f) y = (cos(√sin(x)))…

A: Let's consider  the properties of differentiation.Let f(x) and g(x) are two different function…

Q: Wouldn't tan(x+pi)-(-sin(x)) yield tan(x+pi) + sin(x)) instead of tan(x+pi) - sin(x))?

A: Yes , there is a mistake on that question. I give u correct solution .  tan(x + π) - cos( x + (π/2))…

Q: cos(x1)=-1/3 sin(x2)=2/3 find 1. sin(x1+x2) 2. cos(x1+x2) 3.sin(x1-x2) 4.cos(x1-x2)

A:

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: cos( 2 cos (x/ 12)) = Select one: O None O 24 x / ( 144 + x²) O 2x ( 144 - x² )º.5 / ( 2x² - 144 )…

A: Given cos(2cos-1(x/12))We know that 2cos-1(u)=cos-1(2u2-1)Here upon comparing u=x12

Q: IFS(x) = - sin(x), then S ® (1) is equal to - sin(x) B) - cos(x) sin(x) O cos(x)

A: We have to solve

Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

A:

Q: O find fx) if CoSx @ £(x)=. Sin X O flx) = x-4CSC x+2 Cot X © f(x)= (x).cotx 3- COSX. CSCX

A: SOLUTION-

Q: Evaluate / 4x cos(x)dx

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Q: a sin (cos X) b cos (cos x) c sin (sin x) d cos (sin x) a By expressingy = x in the form y = sin…

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Q: cos2x- sin2 cos2x For dr=F(x) +C What is F(x)? cOSx-sinx A -3 sinx- cosX 2. Cos - COSX+sinPx 3 B…

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Q: Please

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Q: S(csc x cot x + 8x")dx - sin x + x8 + c - sec x + x° + c CSc x + x° +c CSc x + x° +c - sec x + x° +c

A: