If f is the function defined by f(x) = x + cos 2x, then f"(x) = %3D -8sin 2x O -sin 2x sin 2x 8cos 2x 8sin 2r

Q: determine the annihilator of the givenfunction. F(x) = sin2 x cos2 x cos2 2x.

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Q: If f(x) = A B D tanx S™ 0 1+tan²x 1+etanx sec ³x l+etanx In (secx)√1+tan²x 1+etanx sec²x tanx 1+12…

A: Using the Leibnitz rule:

Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

Q: If fx*cos x dx = f(x) - j2xsinx dx, then f(x) is A. 2 sin x + 2x cos x+C B. xsin x +C %3! C. 2x cos…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Is the ODE (sin(x-y)+1)dx=(sin(x-y)-2y)dy satisfied by the implicit solution x+y2=cos(x-y). Show…

A: An implicit function, however, is an equation that defines a relationship between two or more…

Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

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Q: 11. Evaluate f- 2 sin 3x dx 4+cos 3x a.) -2 In 14+cos3x| + C b.) 3 In 14+cos3x| + C c.) - In…

A: Solve by integration

Q: A 61. f(x) = -2 cos (3x); 0 sxs 1/3

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Q: ) Evaluate A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og y s x*

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Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…

A: Given problem:-

Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

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Q: 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…

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Q: Find the critical points of f (x) = 2 cos 3x + 3 cos 2x in [0, 2π]. Check your answer against a…

A: Given: f(x)=2 cos(3x)+3 cos(2x), 0, 2π

Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

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Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

Q: 21. If y=(x* +sin x)", then dy dx (A) 6(x*+sinx) (4x-cos.x) (B) 6(x*+sinx) (4x' +cosx) (C)…

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Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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Q: Find the general solution using Reduction of Order: y''+y'=cos 3x

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Q: If f(x,y,z)=In(x²y+sin² 12

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Q: Let f : R→ R be a differentiable function. Then for all x € R, the derivative of f ( sin (4x)) with…

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Q: Evaluate the integral. (sin Sx cos 5x dx 늘 cos 13x-5 cos 3x + C 26 1 cos 13x - 26 1 sin 13 x + C 26

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Q: If f(x) is odd function then | sin( f(x)) dx = Select one: O 2 : sin(x) dx O None O 2 2 sin( f(x))…

A: To check if a function is even or odd in the given function then apply x=-xIf f(-x)=f(x) then the…

Q: We have determined that g'(x) = 2 and h'(x) = cos(x), where g(x) = 2 In(x) and h(x) = sin(x).…

A: Our Objective is to find the derivative.

Q: If f(x) = sin(x)e2x, then f"(x) = A) 3sin(x) e2x + 4cos(x) e²*. B) 3sin(x) e2x + 2cos(x) e²x. C)…

A: The given function is: f(x)=sin(x)e2x to find the second derivative f''(x). For that one has to find…

Q: Evaluate the integral cos"() sin(x) dæ cos'4 using the substitution u = 1 = cos(x). | cos"(x) sin(x)…

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Q: Find the critical numbers of the function

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Q: Find f'(x). f(x) = = O V 10x - sin²(7x) 1 f'(x) = = 2√/10 - 14cos(7x) 1 f(x) 2√10x - sin² (7x) 10…

A: This question is related to differentiation, We will solve it using given information.

Q: Find the root of f(n) = 3x - cos(x) -1 = 0

A: Please rate and feel free to ask any query about any part.

Q: If f(x) = 4c0s(x) , then f'(x) = %3D (A) – sin(x) 4°os(x) (B) – In(4) sin(x) 4cos(x) (C) In(4)…

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Q: Find the critical numbers of the function. b) g(x) = |2x + 3|| c) f(e) = 2 cos 0 + sin2 0 d) f(x) =…

A: gx=2x+3 fθ=2cosθ+sin2θ fx=x lnx

Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

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Q: y" +y' = cos 3x

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Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: Thus, for u = g(x) = sin(5x), %3! f'(g(x)) = F'(sin(5x)) = 8 %3D %3D 8 Next we calculate g'(x). g(x)…

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Q: If f x?cos x dx = f(x) – S 2xsinx dx, then f(x) is _ A. 2 sin x + 2x cos x + C B. x²sin x + C C. 2x…

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: 6) Find most general antiderivative of the fxn ) f(2) = secx (secx +tane) Secx +tanx, = secx COS X

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Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C

Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: Find f'(x): f(x) = sin(2x) O 4sin (2a) (2 ln 4) cos(2x) O 4sin (2x) (2 cos(2x)) O 4sin (2x) (In 2)…

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Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: If f (x) = A) B (C) D tanx √1+1² 1+e' 0 1+tan²x tanx 1+e sec ³x -dt, then f'(x) equals tanx 1 + e In…

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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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Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

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Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.

Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

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