1 Let f(x) = (5 sin x + 8 cos a)tan f'(x) =

Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: Determine the absolute extreme values of the function f(x) = sinx - cosx + 6 on the interval 0 ≤ x ≤…

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Q: If f(x) = cos x – 7 tan æ, then f'(z) -sin( x ) – 7 sec²(x) = f'(2) =

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Q: 5. tan (x)dx 1 -dx cos² (x) sin () 6.

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Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

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Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

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Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x & cos-1x

Q: find dydx 15. y = (sec x + tan x)(sec x - tan x)16. y = x^2 cos x - 2x sin x - 2 cos x17. ƒ(x) = x^3…

A: To Determine: find the derivative  Given: we have y=secx+tanxsecx-tanx Explanation: we have…

Q: 28. The derivative of In(x sin x) is 1. 1 + cotx а. b. C. d. tan x +x - +x sinx

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Q: 1 Let f(x) (5 sin x + 4 cos x æ)tan- f'(x) =

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Q: 1. Differentiate the function. y = In(VT sin-(5æ))

A: As per our guide lines we can answer only 1 question. Kindly post the other question seperately.…

Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: 3 cos(x) sin(4x) 3. lim x→0 2x

A: Solution:

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Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: Compute integral sin(cos(x^2)) sin(x^2)x dx

A: Explanation is given below...

Q: f(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

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

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Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: elin (sin x+ cos x) dx 1. S ecosx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: 1+sin 2 x 1) Find the derivative of f(x) 2 cos3 x

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Q: Find the smallest positive zero of f(x)=cos^2(x)-sin^2(x)

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Q: lim (x approaches 0) of [sin(5x)cos(6x)]/(x)

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Q: roo sin(2) Compute (4) dx. fo x(x²+4)

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Q: (3 tanx-2 cos y)sec" xdx + tanxsin yay = 0

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Q: S tanx 1+ COS X JX

A: Given problem:-  ∫tan(x)dx/(1+cos4(x))

Q: 1-sin x dx 1-cos x 2

A: Introduction :

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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

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Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…

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Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

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Q: )Find the anti derivative for sin(x^2) 2x

A: we have to find the anti derivative of ∫sinx22xdx...............1 first we put in place of x2 =z…

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: 7. Find the derivative with respect to x of tan-(2) – In(2.r +3) = 4 cos (2y +5). %3D

A: To find the derivative of tan-1x2-ln2x+3=4cos32y+5. Solution: Power rule of differentiation states…

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: The derivative of f(x) = ln( is cos x - Select one: O f'(x) = sinx O None of the other options O…

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Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: x sin 2x sin cos x 2 X. Prove that 8 dx 2х - л

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Q: 15. f(x)= sin 3x 17. f(x)= tan 2.x 19. f(x)= 3 cos (x – 7/2) -

A: 15) For sin(3x) the range of the function will  be the same as sin(x) just the period, in this case,…

Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

Q: a(cos2x) sin(x-) TC 1. f(x) = tanx 4. What values should a and b take for the function fx) to be…

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Q: Compute f sin(cos(x²)) sin(x²)x dx

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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