Differentiate each function a) y = Cos³ x b) y = Sin(x³) c) y = Sin²xCos3x

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  1. Calculus

    Differentiate each function a) y = Cos³ x b) y = Sin(x³) c) y = Sin²xCos3x
  2. Calculus grade 12

    differentiate the function ( a) y = cos³x b) y = Sin²xCos3x c) y = Sin (x³)
  3. Calculus grade 12

    differentiate the function a) y = cos³x b) y = Sin²xCos3x c) y = Sin (x³)
  4. trigo help!

    1. differentiate cos(3/x) 2. differentiate sin(4/x) 3. differentiate 3/{sin(3x+pi)} 4. differentiate pxsin(q/x)where p and q are constants. 5. differentiate xsin(a/x) where a is constant 6. differentiate sec^3(3x^2+1)
  5. trigonometry

    Verify that following are identities: 1. cos 3t = 4 cos³ t-3 cos t 2. sin 4x = 8 sin x cos³ x-4 x cos x (use a double-angle identity)
  6. math

    can some one please help me with the following questions as i don't understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) (b)write down the derivative of each of...
  7. Calculus

    How would you differentiate each function? 1.) v(t)= sin^2 (sqrt (t)) 2.) h(x)= sin x sin 2x sin 3x
  8. Math

    Guys please help me with this Trigonometry question based on De Moivre's theorem. Q: Find ¦È such that 0¡Ü¦È¡Ü360. cos7¦È + cos3¦È = cos5¦È I attempted to solve it with limited knowledge but I kind of doubt my answer. Anyway, this is how I did it : 1) [cos7...
  9. pre cal verifying identities

    how do I verify?? sin(x)+cos3(x)=sin(x)-3cos(x)+4cos^(3)x
  10. Calculus

    differentiate each function a) y = cos^3x b) y = sin(x^3) c) y = sin^2 xcos3x
  11. Differentiate

    Can someone please differentiate y = sin x / x for me? What I did was put (sin x)(x)^-1 and used the product rule... So for me it was (sin x)[-1(x)^-2] + [(x)^-1(cos x)] Now as I'm looking at a similar homework problem I think my method may be wrong... If my method is wrong it...
  12. Derviatives

    Differentiate the function. f(x) = sin(5 ln x)
  13. cal

    Differentiate the function. f(x) = sin(7 ln x)
  14. Cal

    Differentiate the function. f(x) = sin(x) ln(2x)
  15. Maths - Calculus

    Can anyone help with this...I need to find the derivative of the functions below. If possible please show working so I can try and understand? f(t) =3-t^4 and g(t)=sin(4t) Then using the Quotient Rule differentiate the function k(t) 3-t^4/ sin(4t) (0<t< pie)
  16. Maths - Calculus

    Can anyone help with this...I need to find the derivative of the functions below. If possible please show working so I can try and understand? f(t) =3-t^4 and g(t)=sin(4t) Then using the Quotient Rule differentiate the function k(t) 3-t^4/ sin(4t) (0<t< pie)
  17. Calculus

    Differentiate the following function. f (x) = 7 sin(x) + 1/6 cot(x)
  18. Mathematics

    (sin 4x cos 3x)^2 differentiate the following function
  19. calculus

    Differentiate the following function. f (x) = 6 x 2 sin(x)tan(x) Where do I begin?
  20. Calc.

    Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1...
  21. calculus

    Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1...
  22. Math

    Prove the identities 1. cos3Ɵ + cos Ɵ = 4cos^Ɵ - 2 cos Ɵ 2. sin (A+B)sin (A-B)=cos2B + sin^2 A-1
  23. math

    Eliminate the parameter (What does that mean?) and write a rectangular equation for (could it be [t^2 + 3][2t]?) x= t^2 + 3 y = 2t Without a calculator (how can I do that?), determine the exact value of each expression. cos(Sin^-1 1/2) Sin^-1 (sin 7pi/6) x= t^2 + 3 y = 2t ...
  24. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then.
  25. calculus

    5. Find the equation of the tangent line to the graph of f(a) = -sec(a) at the point (0, -1) 6. Differentiate y = sin(x)tan(x). 7. Find f '(x) for f(x) = sin(x)cot(x). 8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9. Find f '(x) for f(x) = xln(x) - 5ex.
  26. Math (Calculus)

    Hello, I have a difficulty with the following question. The question is asking to find the slope of the tangent at x=3 for this function: f(x)=4x^3/sinx. X is measured in radians. The is the derivative of f(x): f'(x)=(12x^2)(sinx)^-1 + (4x^3)(-1)(sinx)^-2(cosx) When x=3 is ...
  27. Calculus - please check my work

    differentiate each function a) y = cos^3x b) y = sin(x^3) c) y = sin^2 xcos3x my answers: a) y' = 3cos^2 x(-sinx) b) y' = cos(x^3)(3x^2) c) for this one, i don't know which one is correct. i got 2 different answers but i think they may be the same.. im not sure, i did it twice...
  28. Calc

    1. Differentiae each function a) Y=-3x^2+5x-4 b) F(x) = 6/x-3/x^2 c) F(x)=(3x^2-4x)(x^3+1) 2. Determine the equation of the tangent line to the curve y=2x^2-1 at the point where x=-2 3. Evaluate, rounding to two decimal places, If necessary a) In 5 b) b) in e^2 c) (ine)^2 4. ...
  29. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...} (3) sin (1/x)=-1 (4) Explain ...
  30. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...} (3) sin (1/x)=-1 (4) Explain ...
  31. Calculus - Differentiate

    Differentiate y= (sin(x)) / (x^4) y' = ?
  32. Maths

    Differentiate (sin^3)x and use this result to evaluate the integral of sin^2 x cos x dx between pi/2 and 0. Thanks!
  33. Calculus

    I think I have the correct answers for the following problems. For anyone who has the time I would appreciate it if you could tell me if I am correct/incorrect. Thank you. 1). Differentiate ã(x)sin x = (2xcosx+sinx)/2ã(x) 2). Differentiate 2t/(4+t^2) = (8-2t^2)/(4+t^2)^2...
  34. Math

    1. On the interval [0, 2pi] what are the solutions to the equation sin3xcos2x = -cos3xsin2x + 1? pi/10 and pi/2? 2. What is the value of tan75degrees? √(3) + 1)/(1 - √(3))? 3. Value of cos(130degrees)cos(130degrees) + sin(10degrees)sin(10degrees)? Not sure 4. On ...
  35. Math

    The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D) f(x)=8 sin x/2-3
  36. Calculus

    How do I graph sin and cosin example: graph y=-4sin(x + 3.14) Your function is the sin function shifted by pi units to the left. You need to study the sin function and know how to graph it. There should be a picture of it in your text, it's a very commonly used funtion that ...
  37. Calculus

    Hello, Could somebody kindly check my answer for the following question? Find the derivative of the following function: h(x)=3e^(sin(x+2)) h'(x)=3'(e^(sin(x+2))+3(e^(sin(x+2))' h'(x)=0(e^(sin(x+2))+3(e^(sin(x+2))(cos(1)) h'(x)=3cos1(e^(sin(x+2)) I would greatly appreciate your...
  38. Calculus

    Hi, I'm having trouble using implicit differentiation to determine dy/dx in the form dy/dx = f(x,y) for sin(2x+3y)=3x^3y^2+4 Do I make it sin(2x+3y)-3x^3y^2=4 then differentiate to get 2cos(2x+3y)-9x^2*2y=0 ? I'm a little lost... Any help appreciated.
  39. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then. How would I show the sequence of values, any help would be greatly ...
  40. MATH

    hi i was just wondering if u could help me with this math problem. find dy/dx at the indicated point in two different ways (a)solve for y as a function of x and differentiate (b) differentiate implicity. 1. y^2=3x+1 (5, -4) how do u do this in two ways? im confused. and whats ...
  41. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4. Find all values of x on the graph of f(x) = -2x3...
  42. math help

    I really don't understand how to write the expression as one invloving only sinϴ and cosϴ sin2ϴ+cos3ϴ
  43. MATH

    The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D) f(x)=8 sin x/2-3 I think...
  44. MATH

    The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D) f(x)=8 sin x/2-3 I think...
  45. MATHS...PLEASE HELP

    Differentiate sin(cubed)x with respect to x. Hence find (integration sign) sin(squared) x cosx dx. ALSO Find the equation of the tangent to the curve y = 2 sin(x-(pie divided by 6)) at the point where x = (pie divided by 3) .
  46. physics

    Given the position function s(t) = t cos t, find the velocity function. Answer v(t) = -sin t v(t) = sin t v(t) = cos t - t sin t v(t) = cos t + t sin t
  47. Calculus

    1) The period of a trig. function y=sin kx is 2pi/k. Then period of y=sin^2(pi.x/a) should be 2pi/(pi/a)=2a, but somewhere it is given as a. Which is correct? 2) The period of r=sin^3(theta/3) is given as 3pi. How is it worked out? Is it because after theta=0, the function ...
  48. calc

    what is the derivative of sinx- cosy = 0 in its simplest form? I got to the point y'=-consx/siny, but I wasn't too sure. This could probably simplified further. help! You're supposed to treat y as a function of x and differentiate it implicitly. We have d/dx{sinx- cosy)=d/dx{...
  49. math

    Hi, I am in need of some help. How would I find the derivative of the function: f(x) = int e^sin(t) dt if the upper bound is x^2 and the lower bound is cos(x)? I'm not really sure what to do here since e^sin(t) is not an integratable function. Should I instead integrate the ...
  50. calculus

    differentiate y=x sin((4)/x)
  51. Calc

    Differentiate f(x) = ln(x)/sin(x)
  52. Math

    Find y'(x) when cos y - y^2 = 8 a) -siny - 2y b) - (1/sin y - 2y) c) 0 d) - (8/cos y - y) So if I implicitly differentiate: y'(x) = -sin(y) - 2y y' = 0 Am I right to say that there's nothing more you can do to this and pick C? y' = 0 / (-siny - 2y) So y'(x) = 0?
  53. MATHS

    In the values interval [0, 2p] the function f (x) = sin(x) has more periods by the function g (x) = sin(3x). True or False?
  54. Calculus

    Differentiate: y=sin(2z)+cos^2z
  55. Calculus

    Differentiate with respect to x 1/sin x
  56. Math

    In obtuse triangle PQR, P=51 degrees, p= 10cm, and the longest side, q=12cm.Draw the triangle and solve for Q to the nearest degree. I did, 10/sin 51=12/sin Q 10(sin Q)/10=12(sin 51)/10 Q= 2nd function sin 0.9325751 Q=68 degrees Q=180-68 Q=111 degrees
  57. Calculus AP

    5.2 The Natural logarithmic function Differentiate the function problem # 13: f(x)= sqrt(x) Inx
  58. integral calculus

    integrate. (1):sin2xcos3x (2):5(cos3x)^2
  59. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) Add the two equations: sin(a+b) + sin(a-b) = ...
  60. Differentiation

    How do i differentiate cos(3/x) or sin(4/x)? Please help!
  61. Calculus :(

    Differentiate with respect to (t). y = d cos(t) + (t^2)sin(t)
  62. Math

    This one confused me since it revolved around what seemed like dividing trig function by another function Write the following expression in terms of the tangent function 2 / ((cos(r^2 - s^2) / (sin(r^2 - s^2)) = ? I know tan t = sin t / cos t. So would I multiply by the ...
  63. Adv function

    sin(7x)= sin(x)[cos^2(3x)-sin^2(3x)]+2cos(x)cos(3x)sin(3x) I tried for an hour but still don't know how. Plzz help
  64. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 x = (sin^2x)^3 + (cos^2x)^3 = (sin^2x+cos...
  65. MATH

    Determine all the absolute extreme values for the function f(x, y) = sin x sin y sin(x + y) on the square 0 <x <PI ,0 < y < PI.
  66. calculus

    Determine all the absolute extreme values for the function f(x,y) = sin(x)*sin(y)*sin(x+y)on the square 0<x<pi, 0<y<pi
  67. Calculus Help and Check

    find the derivative of the function integral from cosx to sinx (ln(8+3v)dv) y'(x)= (sin(8+3((sin(x)))+x)+sin(8+3sin(x)-x))/2 Is this the right answer?????
  68. Calculus

    Differentiate. cos^3x My answer: -3cos^2x sin^2x
  69. trigo

    find the period, amplitude,zeros, extreme points at maximum and minimum of the given function: 1.y = sin( -2x) 2.y = 4 sin( 5x) 3.y = -3 sin (3x/5) 4.y = 1/2 cos (-4x)
  70. calculus

    1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (5xCos3x) dx I Will be happy to critique your thinking on these. 1) Derive a recursive relation. 2) Simplest by replacing sin(bx) by Exp[i b x] and taking imaginary part at the end. 3) First integrate sin(yx) ...
  71. Maths

    Please Help Differentiate Sin sqrt x from first principles
  72. algebra

    Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2 sin A I hope this will help. in my algebra ...
  73. Calculus

    I'm having problems with this one. Can't get the right answer. Differentiate the following using the chain rule. f(x) = squareroot(x^2+1)/(3x+1) I know that I can take the whole thing and put it to the (1/2) and differentiate that then use the quotient rule to differentiate ...
  74. Math Exam Review: Limits

    Differentiate: y = sin(2x - 1) + cos(x^3) - tan(3x)
  75. Calculus

    differentiate: y=sin^2(x)- cos^2(x) I have this: y'= 2cosx + 2sinx What do i do next??
  76. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y)(sin^2y) / (sin^...
  77. Quantum mechanics, eigenfunctions!

    Determine if the function sin(x)*e^(ax) where a=constant is an eigenfunction of the operators d/dx and d^2/(dx)^2 Okay. My understanding is that you use the operator and perform its "thing" on the function. In this case, you will have to find the 1st derivative of sin(x)*e^(ax...
  78. Calculus

    THANK YOU TUTORS SO MUCH FOR YOUR HELP Determine the intervals on which the function is concave up or concave down. I finally understand that when f'' is greater than 0 it means concave up. f(X) = 18x^2 + x^4 so I differentiate that to be 36x + 4x^3 that is f' if I ...
  79. calculus

    f(x) = x^2 g(x) = e^2x h(x) = ln(2x) which function is increasing the fastest when x = 2 How do I do this? TIA I will assume that g(x) = e^2x = e^(2x) and now e^x * x . It is ambiguous the way you have written it (1) Differentiate each function to get f'(x), g'(x) and h'(x) (2...
  80. Integral calculus

    Please can anyone help with the following problems - thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these integrals is using partial integration. So, look ...
  81. Trigonometry

    Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^2-4csc=1 My attempt: 3(cos^2/sin^2)-4/sin=1 3(cos^2/sin^2) - 4sin/sin^2 = 1 3cos^2 -4sin =sin^2 3cos^2-(1-cos^2) =4sin 4cos^2 -1 =4sin Cos^2 - sin=1/4 (1-sin^2) - sin =1/4 -Sin^2 - sin =-3/4 ...
  82. calculus

    Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative of sin[sinx]. And multiply that by ...
  83. trigonometry

    (a) If è is in standard position, then the reference angle è is the acute angle formed by the terminal side of è and the ---Select--- x-axis y-axis . So the reference angle for è = 120° is è = ?°, and that for è = 210°is è = ? degrees. (b) If è is any angle, the ...
  84. Math/Calculus

    How would I integrate the following by parts: Integral of: (x^2)(sin (ax))dx, where a is any constant. Just like you did x^2 exp(x) below. Also partial integration is not the easiest way to do this integral. You can also use this method. Evaluate first: integral of sin(ax)dx...
  85. math;)

    Show that sin(x+pi)=-sinx. So far, I used the sum formula for sin which is sin(a+b)=sin a cos b+cos a sin b. sin(x+pi)=sin x cos pi+cos x sin pi I think I am supposed to do this next, but I am not sure. sin(x+pi)=sin x cos x+sin pi cos pi If that is right then I am not sure ...
  86. math

    Differentiate the function f(x) = In(2x +3)
  87. calculus

    Differentiate the function. f(x)=3x ln 6x - 3x
  88. Calculus

    Differentiate the function. y = e^(x+2)+8 y'=?
  89. calculus

    Differentiate the function. f(x) = e^7
  90. Calculus1

    Differentiate the function. y = ((4x^2 + 8x + 4)÷√(x)) x
  91. calculus

    Differentiate the function.((x^2)-((3x^2)(ln(4x))))/(x^6)
  92. calc

    i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is given by v(t) = 1 - sin(2pi*t). a. Acceleration a(t...
  93. Math Trigonometry

    Let z be a complex number such that z=2(cos3∘+icos87∘). Then z^6 can be expressed as r(sinα∘+icosα∘), where r is a real number and 0≤α≤90. What is the value of r+α?
  94. Trigonometry

    IM STUCK ON THESE :( 1. What is the equation for shifting the standard sine curve +2 units horizontally? A. y = sin (x + 2) B. y = sin x + 2 C. y = sin x − 2 D. y = sin (x − 2) 3. What is tan-¹ √3/3 ? A. π/4 B. -π/3 C. π/6 D. -π/4 4. cot...
  95. Trigonometry

    IM STUCK ON THESE :( 1. What is the equation for shifting the standard sine curve +2 units horizontally? A. y = sin (x + 2) B. y = sin x + 2 C. y = sin x − 2 D. y = sin (x − 2) 3. What is tan-¹ √3/3 ? A. π/4 B. -π/3 C. π/6 D. -π/4 4. cot...
  96. calculus

    Differentiate the function f(x) = 186.5
  97. calculus

    Differentiate the following function. A(s)=-19/s^5
  98. calculus

    Differentiate the following function. (7x-5)(3x+9)
  99. Calculus

    differentiate the function R(x)=sqrt(10)/x^7
  100. Calculus

    Differentiate the following function? g(x)=x^2=1/x^2-1
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