# Use implicit differentiation to find an equation of the tangent line to the curve. sin(x+y)=4x−4y at the point (π,π). Tangent Line Equation:

138,988 results
1. ## Calculus

Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x) (b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2. (c) Show that there are now points (x,y) on the curve where the line tangent to the curve is

2. ## Math

In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, consider joining the

3. ## Math

The line has equation y=2x+c and a curve has equation y=8-2x-x^2. 1) for the case where the line is a tangent to the curve, find the value of the constant c. 2) For the case where c = 11, find the x-coordinates of the points of intersection of the line and

4. ## Calculus

a)The curve with equation: 2y^3 + y^2 - y^5 = x^4 - 2x^3 + x^2 has been linked to a bouncing wagon. Use a computer algebra system to graph this curve and discover why. b)At how many points does this curve have horizontal tangent lines? Find the

5. ## calc

Find an equation of the tangent line to the curve at the given point. y = 6 x sin x P= (pi/2 , 3pi) i know the slope of a tangent line is equal to the first derivative. For that I got 6xcosx + 6sinx but idk how to put that into the y-y1=m(x-x1) formula to

6. ## calculus

Use implicit differentiation to find an equation of the tangent line to the curve. sin(x+y)=4x−4y at the point (π,π). Tangent Line Equation:

7. ## calculus

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 2xy − y2 + x = 17, (3, 5) (hyperbola)

8. ## AP AB Calculus

Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the curve. Using the tangent line

9. ## re: Differential Calculus

Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation. x^2cos^2y - siny = 0 Note: I forgot the ^2 for cos on the previous question. Sorry.

10. ## math

Use implicit differentiation to find the equation of the tangent line to the curve xy3+xy=14 at the point (7,1) . The equation of this tangent line can be written in the form y=mx+b i don't seem to no how to find m or b

11. ## Calculus

A) The point p(3,1) lies on the curve y= square root x-2. If Q is the point (x, square root x-2) use your calculator to find the slope of the decant line PQ for the following values of x 1) 2.5 2.) 2.9 3.) 2.99 4.) 2.999 5.) 3.5 6.) 3.1 7.) 3.01 8.) 3.001

12. ## Calculus

Use implicit differentiation to find an equation of the tangent line to the curve at the given point x^2 + xy + y^2 = 3, (1,1)

13. ## calculus

-find the equation of the tangent line to the curve y=5xcosx at the point (pi,-5pi) -the equation of this tangent line can be written in the form y=mx+b where m= and b= -what is the answer to m and b?

14. ## Calculus 1

Find the equation of the tangent line to the curve y=6xcosx at the point (pi,-6pi) The equation of this tangent line can be written in the form y=mx+b What is m ? What is b ?

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P.

16. ## calculus

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve at point P. Find the

17. ## Calculus

I just need the 3rd part!!! (2 points) Let y be defined implicitly by the equation ln(2y)=5xy. Use implicit differentiation to find the first derivative of y with respect to x. dy/dx= 5y^2/(1-5xy) (I ALREADY GOT THIS) Use implicit differentiation to find

18. ## Calculus 1

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2/3 +y^2/3 =4 (-3sqrt(3),1) (astroid)

19. ## Calculus

Use implicit differentiation to write the slope-intercept equation of the tangent line to the graph of (x^2+4)y=8 at the point (2,1):

20. ## Calculus

How do you use imlicit differentiation to differentiate e^(xy)? I have the problem "use implicit differentiation to find dy/dx. e^(xy)+ x^2 - y^2 = 10. I've gotten to the point whereI have d/dx(e^(xy)) + 2x - 2ydy/dx = 0, but I can't go any further because

21. ## Calculus

Find the equation of the tangent line to the curve (piriform) y^2=x^3(4−x) at the point (2,16−−ã). a. Find dy/dx at x=2. dy/dx= b. Write the equation of the tangent line to the curve.

22. ## Calculus 1

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+2xy-y^2+x=6 , (2,4) (hyperbola)

23. ## math

use implicit differentiation to find the slope of the tangent line to the curve (y)/(x-7y)=x^6+5 at the point (1,6/43)

24. ## Math

Use implicit differentiation to find the slope of the tangent line to the curve y/( x + 4 y) = x^4 – 4 at the point (1,-3/13)

25. ## calculus; implicit differentiation

Use implicit differentiation to find the slope of the tangent line to the curve at the point (4,1) -1x^2 - 4xy + 3y^3 = -29 I differentiated both sides and solved for dy/dx and got 2x-4y/9y^2-4x. Then I plugged in X and Y and got -4/7 but when i enter my

26. ## calculus

find an equation of the tangent line to the curve at the given point. graph the curve and the tangent line y=x/x-1 at (2,2) )

27. ## calculus

Use implicit differentiation to find an equation of the tangent line to the curve 3xy^3+4xy=63 at the point (9,1)(9,1).

28. ## maths

find the equation of the tangent to the curve 3xy^2 -4+2y=29 at the point (1,3)using implicit differentiation.

29. ## Math / Calculus

Use implicit differentiation to find an equation of the tangent line to the cardioid at the point (0,0.5) x^2+y^2=(2x^2+2y^2-x)^2 Y=

30. ## Calculus

Use implicit differentiation to find the slope of the tangent line to the curve y/(x+7y)=x^5+7 at the point (1,(-8/55). can anyone help me work out the problem step by step? y (x+7y)-1 = x5 +7 dy(x+7y)-1-y((x+7y)-2*(dx +7dy)=5x4 multiply it out, gather the

31. ## Calculus AB

Find the equation of the line tangent to the curve at t=pi/3: a) x=t-sin(t) b) y=1-cos(t)

32. ## 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

33. ## Calculus

Find the equation of a TANGENT line & NORMAL line to the curve of x^2+y^2=20such that the tangent line is parallel to the line 7.5x – 15y + 21 = 0

34. ## math calculus

Use implicit differentiation to find the equation of the tangent line to the curve xy^3+2xy=9 at the point (31). The equation of this tangent line can be written in the form y=mx+b where m is

35. ## Calculus

(y/(x+9y))= (x^2)-7 at the point (1, -6/55) Use implicit differentiation to find the slope of the tangent line to the curve

36. ## Math (Implicit Differention)

use implicit differentiation to find the slope of the tangent line to the curve of x^2/3+y^2/3=4 at the point (-1,3sqrt3)

37. ## Calculus

If ln(x^2-15y)=x-5+5 and y(-4)=1 find Y prime(-4) by implicit differentiation thus the equation of the tangent line to the graph at the point (-4,1) is y=

38. ## Calculus

Use implicit differentiation to write the slope-intercept equation of the tangent line to the graph of (x^2+4)y=8 at the point (2,1):

39. ## Calc

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (-1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he

40. ## Calculus

Find the exact value of the slope of the line which is tangent to the curve given by the equation r = 2 + cos θ at theta equals pi over 2 . You must show your work. (10 points) Please check if this is right. I put a lot of work into this please check! x=

41. ## maths

given the equation of the curve as y=8-2x^2 (a) find equations of tangent and the normal to this curve at the point where x=a. (b) find the value of a for which this tangent is parallel to the line with equation 3x-y+6=0

42. ## Math

Suppose f(x)=5/(x-2). f'(5)=-5/9. Use this to find the equation of the tangent line to the curve y=5/x-2 at the point (5,(5/3)). write your answer in the form y=mx+b where m is the slope and b is the y-intercept. The equation of the tangent line is.....

43. ## math

Find the equation of the tangent line to the curve y=5xcosx at the point (pi,–5pi). The equation of this tangent line can be written in the form y=mx+b where m= and b=

44. ## Math - Calculus Question.

hey can someone explain to me the relationship between the chain rule and implicit differentiation? It would be very much appreicated, thanks The chain rule is utilized whenever you have a function within a function such as cos^2 x or (5x+1)^1/2. Implicit

45. ## Calculus

the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a) find all points on the curve whose x-coordinate is 1 and write an equation for the tangent line of each of these points b)find the x-coordinate of each point on the curve where the

46. ## calculus

Use implicit differentiation to find an equation of the tangent line to the curve sin(x+y)=2x−2y at the point (π,π). Tangent Line Equation:

47. ## COLLEGE CALCULUS.

Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=5 at the point (4,1) . The equation of this tangent line can be written in the form y = mx+b where m is:? and where b is:?

48. ## Calculus

Use implicit differentiation to find an equation of the tangent line to the curve y^2 = x^3 (26 − x) at the point (1, 5).

49. ## calculus

use implicit differentiation to find an equation of the tangent line to the curve at the given point. 9x^2+xy+9y^2=19, (1,1) (ellipse)

50. ## Calculus

I am unsure of how to take the derivative of this equation. It may be the exponents that are giving me trouble but I'm not sure exactly. Find the equation of the tangent line to the curve 4e^xy = 2x + y at point (0,4). On the left side, is the "xy" the

51. ## calculus

Alright so implicit differentiation is just not working out for me. Use implicit differentiation to find the slope of the tangent line to the curve at point (4,1). y / (x-2y) = x^3 + 4 Tried quotient rule to get the derivative of the left side, then got

52. ## Math, Calc

Use implicit differentiation to find an equation of the tangent line to the curve at the given point x^2+2xy+4y^2=12. Point (2,1). (Eclipse)

53. ## Math

Use implicit differentiation to find the slope of the tangent line to the curve y/( x + 4 y) = x^4 – 4 at the point (1,-3/13)

54. ## CAL

use implicit differentiation to find the slope of the tangent line to the curve (y)/(x-7y)=x^6+5 at the point (1,6/43)

55. ## calculus

Use implicit differentiation to find the slope of the tangent line to the curve (y/x+8y)=x^8 +9 at the point (1,10/-79).

56. ## Rodriguez

use implicit differentiation to find the slope of the tangent line to the curve of x^2/3+y^2/3=4 at the point (-1,3sqrt3)

57. ## Math (Calculus)

Use implicit differentiation to find the slope of the tangent line to the curve y/(x–9y)=x^6–2 at the point (1,-1/-8). Can someone please help me? I don't understand

58. ## Calculus AP

implicit differentiation Find the slope of the tangent line to the curve xy^3 + 2y - 0.76 =0 at the point (-3, o.7) I'm lost. so 3xy^2 * y' + 2y = 0 right?

Use implicit differentiation to find the slope of the tangent line to the curve at the point (1,3) -4x^2+4xy-2y^3=-46 m=____? ty guys so much!

60. ## math

Given the curve of C defined by the equation x^2 - 2xy +y^4 =4. 1) Find the derivative dy/dx of the curve C by implicit differentiation at the point P= (1,-1). 2) Find a line through the origin that meets the curve perpendicularly.

61. ## Implicit Differentiation

Use implicit differentiation to find the slope of the tangent line to the curve y/x+6y=x^2–6 at the point (1,–5/31) . Again i think i'm messing up with the algebra here. I used quotient rule to get [(x+6y)(y')-(y)(1+6y')]/(x+6y)^2=2x I don't know how

62. ## Math Cal

Use implicit differentiation to find an equation of the tangent line to the cardioid at the point (0, 0.5). x^2 + y^2 = (2x^2 + 2y^2 - x)^2

63. ## Calculus

using implicit differentiation find the equation of the tangent line to the graph of the following function at the indicated point x^2 y^3 -y^2+xy-1=0 at (1,1)

64. ## Calculus

Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write an equation for the

65. ## Calculus AB

Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is no point on the graph of

66. ## Calculus (Math 2A)

Use implicit differentiation to find the slope of the tangent line to the curve y/(x-2y) = y^3 +9 (1,10/21) ive done this problem around 10 times and i still cant get it.... when i did it the last time i got -9-y^3/ 3y^2 x - 8y^3 - 19 and the slope around

67. ## math

1 A particle is moving in a stright line with the position at any time t is given by s= t³–9t²+3t+1,where s in meters and t in second. Find its position and acceleration when velocity is ¯24m/s 2. Given that x²cos y_sin y=0,(0,π). A. Verify that the

68. ## Pre-Calculus

Find the slope of the tangent line to the curve √(1x+2y) + √(1xy) = 8.24 at the point (2,8)? I know you have to use implicit differentiation, but the radicals keep making me mess up algebraically. Is the changing the radicals to exponents the fastest

69. ## calculus

Use implicit differentiation to find the slope of the tangent line to the graph of 18*x^(1/2)+5y^(1/2)+14 at(81/324,1)

70. ## Calculus

If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x + . Check your answer for

71. ## carter

suppose f(x) = (4/5)x^2 + cosx for x≥0 and g is the inverse of f. find g'(1.5) to the nearest thousandth. would I just swap x and y and then find the derivative of that equation to find g'(x) and then plug in g'(1.5)? When I swapped x and y I got

72. ## calculus

carter suppose f(x) = (4/5)x^2 + cosx for x≥0 and g is the inverse of f. find g'(1.5) to the nearest thousandth. would I just swap x and y and then find the derivative of that equation to find g'(x) and then plug in g'(1.5)? When I swapped x and y I got

73. ## Calculus

Find an equation of the tangent line to the curve at the given point. y = sin(sin x), (pi, 0)

74. ## Differential Calculus

Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation. x^2cos^y - siny = 0

75. ## Math (equation of tangent line)

Consider the implicit equation 2xy-1=(x+y+1)^2 a) Compute and solve for the derivative dy/dx as a function of x and y. b) Find the equation of the tangent line to the graph of the above when y=-1. For part a, I found the derivative being equal -(x+1)/(y+1)

76. ## Calc.

Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, and shade the area under

77. ## Calculus. I need help!

HARDER PARTS WAS 3(x^2+y^2)^2=26(y^2+y^2) Find the equation of the tangent line to the curve (a lemniscate) 3(x^2+y^2)^2=26(y^2+y^2) at the point (-4,2). The equation of this tangent line can be written in the form y=mx+b where m is:? and where b is:?

78. ## math

Find the equation of the tangent line to the curve y=6tanx at the point (pi/4,6). The equation of this tangent line can be written in the form y=mx+b where m is: and where b is:

79. ## Calculus 1

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+y^2=(2x^2+4y^2−x)^2 (0, 0.25) (cardioid)

80. ## Math

Given that x²cos y-sin y=0 ,(0,π): a)verfiy that given point is on the curve. b)use implicit differentiation to find the slope of the above curve at the given point. c)find the equation for tangent and normal to the curve at that point.

81. ## Calculus

Use implicit differentiation to find the slope of the tangent line to the curve 2(x^2) + 2xy + 2(y^3)= -18

82. ## Calculus ap

Use implicit differentiation to find the slope of the tangent line to the curve XY^3 + XY = 5 at the point (3,2) .

83. ## Calculus

Use implicit differentiation to find the slope of the tangent line to the curve –2x^2–2xy–1y^3=–3 at the point (–1–1).

84. ## Calculus

Use implicit differentiation to find an equation of the tangent line to the graph at the given point. x + y − 1 = ln(x^5 + y^5), (1, 0)

85. ## Calculus

Use implicit differentiation to find the slope of the tangent line to the curve sqrt of x + sqrt of y = 8

86. ## Calc

Use implicit differentiation to find the slope of the tangent line to the curve y/(x-2y) = y^3 +9 (1,10/21) ive done this problem around 10 times and i still cant get it.... when i did it the last time i got -9-y^3/ 3y^2 x - 8y^3 - 19 and the slope around

87. ## calculus

Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) with domain (0,pi) , find all points on the curve where the tangent line to the curve is horizontal

88. ## Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive? Negative? Zero? 2) Find an equation of the tangent line to the oven curve at the specified point.

89. ## Math

. Given that x²cos y_sin y=0,(0,π). A. Verify that the given points on the curve. B.use implicit differention to find the slope of the above curve at the given point. C.find the equation of tangent and normal to the curve at that.

90. ## Help Calc.!

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P.

91. ## math

Given the parametric curve x= sin(2t) and y=2 sin(t)+ sin(2t) 1) Calculate the slope of the tangent line at any value of t. 2) Find the tangent line at t= (1/2)(Pi).

92. ## Math- Calc 1

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (-1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he

93. ## math

Find the equation for each tangent line to the curve x^2 - sin y = y+4 where y=0.

94. ## Calculus

Find the equation of the tangent line to the curve at the given value of t: x=sin(t); y=(cos(t))^2; t=(pi/3)

95. ## Need help fast on calc

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P. -when plugging y as

96. ## calc

for the parametric curve defined by x=3-2t^2 and y=5-2t ...sketch the curve using the parametric equation to plot of the point. use an arrow to indicate the direction of the curve for o

97. ## Calc.

sketch the curve using the parametric equation to plot the points. use an arrow to indicate the direction the curve is traced as t increases. Find the lenghth of the curve for o

98. ## Calculus

Find the equation of the tangent line to the curve y=2sinx at the point ((pi/6), 1). The equation of the tangent line can be written in y=mx+b form, where m=sqrt3. What is b?

99. ## Calculus

Use implicit differentiation to find an equation of the tangent line to the curve y^2 = x^3 (26 − x) at the point (1, 5).

100. ## math

Consider the function: (-2x^2 - 2x-4) y = 2x^2 - x +10 Find y â€² using implicit differentiation. Do not solve for y. What is the slope of the tangent at (x,y) = (2,âˆ’1)? Find y â€² by solving for y and using the quotient rule. What is the