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

20,608 results

1. ### Calculus

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

differentiate the function ( a) y = cos³x b) y = Sin²xCos3x c) y = Sin (x³)

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...

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) = ...

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 ...

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) ...

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