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
  7. 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
  8. Calculus

    How would you differentiate each function? 1.) v(t)= sin^2 (sqrt (t)) 2.) h(x)= sin x sin 2x sin 3x
  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. 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)
  12. 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)
  13. 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
  14. cal

    Differentiate the function. f(x) = sin(7 ln x)
  15. Derviatives

    Differentiate the function. f(x) = sin(5 ln x)
  16. Cal

    Differentiate the function. f(x) = sin(x) ln(2x)
  17. Mathematics

    (sin 4x cos 3x)^2 differentiate the following function
  18. Calculus

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

    Differentiate the following function. f (x) = 6 x 2 sin(x)tan(x) Where do I begin?
  20. 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
  21. 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
  22. 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)
  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)
  24. 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 +
  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
  26. 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
  27. 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)=
  28. 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)=
  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
  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
  31. 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.
  32. 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) +
  33. Calculus - Differentiate

    Differentiate y= (sin(x)) / (x^4) y' = ?
  34. 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
  35. 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
  36. 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)
  37. 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!
  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

    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
  40. 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)
  41. 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
  42. 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)
  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)
  44. math help

    I really don't understand how to write the expression as one invloving only sinϴ and cosϴ sin2ϴ+cos3ϴ
  45. 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
  46. 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
  47. 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) .
  48. 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
  49. 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
  50. 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 +
  51. 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
  52. 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:
  53. Calc

    Differentiate f(x) = ln(x)/sin(x)
  54. calculus

    differentiate y=x sin((4)/x)
  55. 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
  56. Math

    Hi, I wanted to know how wanted to know if i was doing this step right for my homework. the question is Given rt=<sin(t)-tcos(t), cos(t)+ tsin(t),t^2 sqrt 3 and the whole thing is divided by two. The question is find the velocity vector and find V(pi)
  57. Calculus

    Differentiate: y=sin(2z)+cos^2z
  58. Differentiation

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

    Differentiate with respect to x 1/sin x
  60. 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
  61. 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
  62. integral calculus

    integrate. (1):sin2xcos3x (2):5(cos3x)^2
  63. Calculus AP

    5.2 The Natural logarithmic function Differentiate the function problem # 13: f(x)= sqrt(x) Inx
  64. 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
  65. 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?
  66. Calculus :(

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

    Please Help Differentiate Sin sqrt x from first principles
  68. 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:
  69. 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?????
  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
  71. 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.
  72. 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
  73. 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)
  74. Calculus

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

    Differentiate. cos^3x My answer: -3cos^2x sin^2x
  76. 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
  77. 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
  78. 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
  79. 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
  80. Math Exam Review: Limits

    Differentiate: y = sin(2x - 1) + cos(x^3) - tan(3x)
  81. 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
  82. Calculus

    Hello, I have some calculus homework that I can't seem to get started..at least not on the right track? I have 3 questions 1. integral of [(p^5)*(lnp)dp] I'm using the uv-integral v du formula So first, I'm finding u and I think it's lnp.......so du is 1/p
  83. 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
  84. 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
  85. Calculus

    Use a Riemann sum with n = 3 terms and the right endpoint rule to approx. ∫(1, 2) sin(1/x)dx. My teacher just needs the terms written out, no need to add or multiply. This is a problem she did up on the board, so here's her answer: sin(4/3)(1/3) +
  86. 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 +
  87. trig help much appreciated! :))

    1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove that tan2  – 1 + cos2 
  88. 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 -
  89. Calculus - Challenge question

    Our teacher gave us this problem as a challenge. Some of us have been working on it for a few days help! Prove that the largest area of any quadrilateral is obtained when opposite angles are supplementary. Wow, what a classic and nice question, haven't
  90. calculus

    Differentiate the function.((x^2)-((3x^2)(ln(4x))))/(x^6)
  91. Math

    Differentiate the following function (1/x)-(2/x^2)+(3/x^3) I got (-9x-3)/x^5
  92. math

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

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

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

    Differentiate the function. f(x) = e^7
  96. Calculus

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

    Differentiate the function. g(x)= x^2(1-2x) g'(x)= i tried doing 2x(1-2x) 2x-4x^2
  98. Calculus1

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

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

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