# derivatives differentiate y=x^7/3 So far I have Y=7/3X Is this all there is to this problem? Using the power rule, you bring the exponent down, just like you did. Then, you subtract one from the given exponent to get the

22,330 results
1. ## Calculus

A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show your working, including any

2. ## Math - Calculus

Problem solving with derivatives. Question: A rectangular sheet of cardboard measures 16cm by 6cm. Equal squares are cut out of each corner and the sides are turned up to form an open rectangular box. What is the maximum volume of the box?

3. ## calculus

let f be the function f(x) = e^(2x^2) find the first four nonzero terms and the general term of the power series for f(x) about x = 0 i tried doing this problem but finding the derivatives gets way too complicated can anyone help??

4. ## Calculus - HELP plz!

Find all of the first partial derivatives of f(x,y,z)=arctan y/xz

5. ## Calculus 2 (Differentiate & Decay Problem)

I have two problems I need help on, can someone show and explain step by step how to do the problems? For #1, how would you differentiate and solve the inital-value problem? For #2, I don't understand what I am doing wrong with the problem..I am sure it is

6. ## child growth development

When the XY genetic code begins to assert itself, A. ovaries begin to differentiate. B. testes begin to differentiate C. estrogen begins to be produced. D. brain development begins to occur more rapidly. I think the answer is C

7. ## Math - Calculus

Problem solving with derivatives. A rectangular box has square base of edge length x cm. Its framework of 12 edges is constructed from wire of total length 36cm. Find: i. the height of the box in terms of x ? ii. the volume of the box in terms of x? ii.

8. ## Calculus-Math

Complete the table. y = f(g(x)) u = g(x) y = f(u) y = (2x − 4)^7 u = y= This problem involves the chain rule of derivatives.

9. ## finding numbers

The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +

10. ## calculus

I have been asked to solve this two different ways. The first way is to use the chain rule and then simplify (which I have already done properly), and the second way is to simplify and then differentiate (not necessarily with the chain rule). I am stuck on

11. ## 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)=

12. ## closing off first quadrant

You are planning to close off the corner of the first quadrant with a line segment 20 units long running from (a,0) to (0,b). Show that the area of the triangle enclosed by the segment is largest when a=b From applications of derivatives...this is really

13. ## math/ calculus

full work out with explanation of this problem please we're working with derivatives and i don't understand it given h(x)= cotx/x find h'(pi/2)

14. ## Science

1.Differentiate between soil permeability and retentivity. 2.Differentiate between chemical factors and biological factors of soil organisms. Please note,I wouldn't be needing any information from: Soil-Wikipedia,the free Encyclopedia. Thanks.

15. ## Calculus

Find the outside and inside functions of the following to find their derivatives: 1) sqrt(2x+9) 2) cos(cos(x)) 3) tan(x) I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the

16. ## Calculus

Which of the following choices will most easily evaluate the integral of [L(x)]/[P(x)] dx, where L(x) is a logarithmic function and P(x) is a polynomial? a) Integrate the polynomial function and differentiate the logarithmic function. b) Integrate the

17. ## calculus

a)find the first partial derivatives of f(x y)= x √1+y^2 b)find the first partial derivatives of f(x,y)= e^x ln y at the point (0,e)

18. ## Math(Urgent)

Differentiate. g(x)=(x^3+1)(3x^2-1) I know that the answer is 15x^4-3x^2+6x but I donot know how to get to this. I was using g'(x) X h(x) + g(x) X h'(x) and I was using the derivatives 3x^2 and 6x but I guess this is wrong. Please help!! Thank you.

19. ## Calculus

Which of the following choices will most easily evaluate integral of [L(x)]/P(x) dx, where L(x) is a logarithmic function and P(x) is a polynomial? a) Integrate the polynomial function and differentiate the logarithmic function b) Integrate the logarithmic

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)=

21. ## calculus

Let f be a function that has derivatives of all orders for all real numbers. Assume f(0)=5, f'(0)=-3, f''(0)=1, and f'''(0)=4. Write the third-degree Taylor polynomial for h, where h(x) = integral of f(t)dt from 0 to x, about x=0 for this part, I got

22. ## Calculus

Hello, I really need help on these two homework problem. >< In problem #1, I believe it is related to the exponential functions and their derivatives section...in Calculus II? So, surely there should be a ln in the solution as well? I would like a step by

23. ## calculus

derivatives differentiate y=x^7/3 So far I have Y=7/3X Is this all there is to this problem? Using the power rule, you bring the exponent down, just like you did. Then, you subtract one from the given exponent to get the new exponent. 7/3 - 1 (which is

24. ## English

between differentiate and derivatives. Which is a verb and which is a noun??

25. ## 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)

26. ## Calculus

Hi~ Thank you for your help! I was trying to work on a problem about Taylor series, but i don't think im approaching the problem the right way. I have to find the fifth order Taylor polynomial and Taylor series for the function f(x) at x = 0. f(x) =

27. ## math

I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you

28. ## convert derivatives of x,y,z, to r, Ɵ,z

convert derivatives of x,y,z, to r, Ɵ,z with chain rule? I want provment rules of converting rectangular derivatives to cylindrical derivatives and and also cylindrical to spherical.I know the rules but I cant prove EQUATIONS.thx alot

29. ## 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

30. ## Calculus: Differentiation

I am having trouble solving these. Could you explain how to do these 3 questions, step by step? That would be helpful! 1. Differentiate y=sin ^-1 (x^2) at x=0.5 . Round to 3 decimal points. 3. Differentiate y= (x^2 +1) tan ^-1 (x) at x=1 7. Differentiate

31. ## Math - Calculus 1

Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4 - (1.1)^2

32. ## Calc

If y=3x^2-2, then dy/d(2x-3)= ? I've never taken derivatives with respect to anything other than a single variable, such as x, y or t, so i'm not sure how to start this problem! Thanks

33. ## 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

34. ## calculus

find the second-order partial derivatives of f(x,y)=x^3 + x^2y^2 + y^3 + x+y and show that the mixed partial derivatives fxy and fyx are equal

36. ## Calculus

Okay so I have a question on my assignment that says: You are given that tan(y) = x. Find sin(y)^2. Express your answer in terms of x. I know its derivatives, and I've tried taking the derivatives of both etc, and got them both to come out as cos(y)^2,

37. ## Math - Calculus 1

Approximate the following value using derivatives (without a calculator) (1.1)^4 - (1.1)^2 I only know how to do linear approximation when using square roots. How do I do this type of problem?

38. ## calculus

Differentiate y=lnx You ought to have this memorized. y'=1/x for y= ln x dy/dx = 1/x This is the most basic and fundamental of log derivatives. If you are studying Calculus, and the topic is logs, I fail to understand why you asked that question. IS there

39. ## calculus

Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x. Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative. Use the results to find the twelfth and

40. ## Calculus

How do I differentiate ln (2X^2 - 12X + Y^2 -10Y) and the second differentiate it? HELP ASAP is much appreciated

41. ## Calculus

show that the curves r=asin(è) and r=acos(è) intersect at right angles. can you show that the derivatives for each are the negative reciprocal of each other? That is the key. i need more info..i know how to find the derivative...but how will that prove

42. ## engineering mathematic

give that z = f(x,y). use partial derivatives to find δz/δx and δz/δy for xe^xz + z(xy+1)^3-sin x cos^2y=xy/z present your final answer in the simplest form.. please solve this problem....tq

43. ## math

How can the teacher differentiate instruction when teaching number sense or mathematical operations? Please remember differentiate is for all levels (high, medium, low, ESL, and others)

44. ## 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)

45. ## Math

Is it possible to differentiate (60-x)/1.2? I'm thinking the answer would be 1/0 which is not possible but I just want to make sure. No problem. Just do a little algebra first. f(x)= (60-x)/1.2 = 50 - (5/6) x The derivative is df/dx = -5/6 How did you get

46. ## calculus

I am having trouble with this problem also derivative differentiate f(x)=(3-x)^4(x+5)^3 so far I have 4(3-x(x+5)^3+3(x+5)(3-x) Not quite right. Treat it as d/dx[u(x) + v(x)] = u dv/dx + v du/dx u(x) = (3-x)^4 v(x) = (x+5)^3 du/dx = -4(3-x))^3 (using the

47. ## largest possible area

Again from applications of derivatives.. what is the largest possible area for a right triangle whose hypotneus is 5cm long, and what are its dimensions. Thanks a^2 + b^2 = c^2 3^2 + 4^2 = 5^2 Area of a triangle 1/2 base times altitude hint: base is 3

48. ## Math(Please check. Thank You)

1) solve:e^x(x^2-4)=0 e^x=0 and then (x+2)(x-2) so x=2, -2 2) differentiate: y=ln(6x^2 - 3x + 1) 1/(6x^2 - 3x + 1) * 12x-3 3) differentiate: y=e^-3x+2 -3 * e^-3x+2 4) evaluate: 2^4-x=8 2^4-x = 2^3 4-x = 3 -x=-1 so x=1 5) differentiate: x^3 + y^3 -6 =0 3x^2

49. ## Math

Problem solving with derivatives. Question: The sum of 2 numbers is 12. If one number is x, the value of x for which the product of the two numbers is a maximum is?

50. ## math

Differentiate the following function, much like problem 14 of section 3.2 (page 152) of your textbook: y = 14 J + N e^t, where J and N are given constants. Enter the derivative here:

51. ## math

If cos(3 x)6Ó14 x e^2 y=0, find [ dy/dx] using implicit differentiation. In this problem, you should differentiate both sides of this equation with respect to x. First, using implicit differentiation, differentiate the left side of the equation with

52. ## Math - Calculus

Problem solving with derivatives. Question: A piece of wire length of 30cm is cut into 2 sections. Each section is then bent into the shape of a square. Find the smallest possible value of the sum of the areas of the two squares.

53. ## Calculus

How do I solve this problem without integrals or derivatives? Find the distance traveled in 14 seconds by an object that is moving with a velocity of v(t) = 11 + 6cos t feet per second. A. 154.8204 B. 156.1704 C. 159.9436

54. ## appliedcalculus

Suppose a farmer has 1,000 feet of fence and wishes to build two identical rectangular enclosures. What should be the dimensions of each enclosure if the total area is to be a maximum? Set problem up and solve using derivatives.

55. ## Calculus III

Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And

56. ## Calculus III

Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And

57. ## Calculus III

Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And

58. ## optimal dimensions

Applications of derivatives You are planning to make an open rectangular box from an 8 by 15 inch piece of cardboard by cutting congruent squares from the corners and folding up the sides. what are the dimensions of the box of largest volume you can make

59. ## BC Calculus

Solve this problem algebraically, using your knowledge of derivatives. Do not solve by graphing. If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed?

60. ## Calculus AP

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

61. ## Maths

Can someone help me with the following? Prove that (grad)^2 f(r) = D^2/dr^2 + (2/r) Df/Dr Where D^2/dr^2 refers to the second partial derivative of f , w.r.t. r and Df/ Dr refers to partial derivative of f, w.r.t r vector r = xi + yj + zk and f(r) is twice

62. ## micro

hi, i need some help with my econ homework. i know what the law is, basically that more isn't always better. i just need to know how to tell if it applies to a labor equation. my problem goes like this. F(K,L) = K + 10L, write expressions for marginal

63. ## psychology

When the XY genetic code begins to assert itself A ovaries begin to differentiate B testes begin to differentiate C estrogen begins to be produced D brain development begins to occur more rapidly i believe the correct answer is B

64. ## 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

a) determine the derivative of y = sin2x b) determine the derivative of y = 2SinxCosx c) shoe that derivatives in parts a) and b) are equal d) explain why derivatives in parts a) and be should be equal.

66. ## 2nd Order linear ODEs

I'm having trouble solving this problem: For the equation x^(2)y′′ - xy′ = 0 , find two solutions, show that they are linearly independent and find the general solution. Hint: Try y = x^(r). I divided the equation by x^(2) first to simplify it, and

67. ## Calculus

Just got through with derivatives, power rule, and chain rule. I am supposed to find the first and second derivatives of the function. y = 4x/√x+1 and y = cos^2(x) y' = [(x+1)^(1/2)(4)]-[(4x)(1/2(x+1)^(-1/2))(1)] y' =

68. ## 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

69. ## Calculus

I finished this problem but I wanted some feedback because I don't know if it's entirely correct. Suppose that functions f and g and their derivatives with respect to x have the following values at x=2. f(x)=8 g(x)=2 f'(x)=1/3 g'(x)=-3 Find d/dx of f(g(x))

70. ## Writing

Do the words define an differentiate have the same meaning? Because I have to define and differentiate population and community but when I define it doesn't that show the differences between the two words?

71. ## Derivatives

Find the derivatives of: 1. H(x)= sin2xcos2x The answer given is 2cos4x. My question is, how in the world did they get that!? Shouldn't the answer at least contain the sin function, either negative or positive seeing as it's the derivative of cos? Also,

72. ## calculus

Can some explain how to do this problem? I tried using derivatives...but...I keep getting a different answer from what my teacher told me! A projectile is fired directly upward with an initial velocity of 144 ft/sec and its height (in feet) above the

73. ## calc

What are the first and second derivatives of y = (1/x^2)-(1/(x-2)^2)?

74. ## calc

What are the first and second derivatives of y= x^(2/3) * (2.5 - x)

75. ## calc

what are the first and second derivatives for y= x* (4-x^2)^1/2

76. ## Calc

what are the first and second derivatives for y= x* (4-x^2)^1/2

77. ## Calc

What are the first and second derivatives of y= x^(2/3) * (2.5 - x)

78. ## Calc

What are the first and second derivatives of y= x-3x^(1/3)

79. ## calculus

derivatives. f(x)=(1/-7x^12) f'(2)=? f'(-1)=?

80. ## math

I need help differentiating this question: 3e^-4x that's three e to the power of negative 4x. when you differentiate, you get: -12e^-4x thanks, but how come it's not -12e^-4x-1, or do i just not minus a one when the power is a co-efficient? Remember, the

81. ## Calculus

yes! tnk u ok? It's actually (x->0.) Find the limit of cot(x)-csc(x) as x approached 0? Lim [cot(x) - csc (x)] ..x->0 = Lim [(cos x -1)/sin x] ..x->0 Use L'Hopital's rule and take the ratio of the derivatives: Lim (-sin x/cos x) = 0 x->0 thank you very

82. ## 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

83. ## calculus

Anti-Derivatives 2x^6-x^3/x^2

84. ## Maths

Find the derivatives of these: f(x)=√

85. ## Calculus

Compute the derivatives of : f(x)= x^7 + 7^x+ 7^7

86. ## Calculus Homework

You are blowing air into a spherical balloon at a rate of 7 cubic inches per second. The goal of this problem is to answer the following question: What is the rate of change of the surface area of the balloon at time t= 1 second, given that the balloon has

87. ## Math

HELP DERIVATIVES!!!!!!!!!!!!! if h(x)=f[f(x)] use the tables for f and f' to find the value of h'(1) X f(x) f'(x) 1 3 2 2 1 5 3 6 7

88. ## calculus

find the first and second derivatives for 3x^4-4xy^2+7=2y

89. ## Calc

What are the derivatives? Thanks a) y = log(base2)(4-9x) b) y = x^(8x)

90. ## calculus

Find the derivatives of the following function: i)y=-3x^-3 +2x^-2 + x-2

91. ## calculus

x^2+8x+32 its critical points in derivatives

92. ## math

derivatives: y=(x^3+1)^2, then dy/dx is: i got 6x^2(x^3+1) first but im not sure. Can i see the steps of how it is done right. I also got 2(3x^2+1), which one is right?? sorry for bugging.Thanks

93. ## calculus quick question

g(x)= sqrt(1-4x^2) Can someone help me find the first and second derivatives please!

94. ## calculus

find the derivatives F(x)=8ln(x^5-2x)

95. ## calculus

Find the derivatives of the functions k(x)=(x^3+e^x)^4

96. ## English

1. The hospital is for certain people. 2. He has a certain problem. 3. He has a sure problem. 4. He is certain that the boy is diligent. -------------------------- Are they all grammatical? The meaning of 'certain' seems to be different. Does #2 mean #3?

97. ## chemistry

assuming the reaction goes to completion, determine the final concentration of NH4Cl in the calorimeter. NH4Cl(s)+ H2O(l)-> NH4Cl(aq) concentration of NH4Cl is 1.00M its specific heat is 3.93 and density is g/ml. note: the exact same question was asked for

98. ## math (2)

Find the first partial derivatives of the function. f(x,y,z) = xe^(y/z) a. fx = ? b. fy = ? c. fz = ?

99. ## Calculus

I get mixed up when graphing derivatives. If I'm given the graph of f how do I get f' and f"?