Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathcalculus

  • 2 years ago

help please: Use implicit differentiation to find the equation of the tangent line to the curve at the point. (attached below)

  • This Question is Closed
  1. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

  2. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i know i have to use implicit differentiation, then plug into derivative to find slope, plug slope and given points to point-slope formula.

  3. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Problem I have is step 1

  4. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    take the derivative with respect to x. use the product rule for example, on the xy term you do this \[ \frac{d}{dx}xy = x \frac{d}{dx}y+ y \frac{d}{dx}x \\ = x \frac{dy}{dx}+ y \frac{dx}{dx} \\ = x \frac{dy}{dx}+ y\] use the same idea on \(xy^3\)

  5. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i got x(3y*dy/dx) +y^3

  6. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @phi

  7. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so.. 3xy*dydx +y^3

  8. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    dy/dx**

  9. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you mean 3 x y^2 dy/dx for the first part d/dx of y^3 is 3 y^2 dy/dx

  10. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay im lost with the second part.

  11. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i know that you took the derivative of xy^3= 3xy^2

  12. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    +xy= 1?

  13. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    *dy/dx

  14. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    from the beginning \[ \frac{d}{dx}\left(xy^3 + xy = 4\right) \\ x \frac{d}{dx}y^3 + y^3 \frac{d}{dx}x+ x\frac{d}{dx}y+ y \frac{d}{dx}x=\frac{d}{dx}4\] that simplifies to \[ x \frac{d}{dx}y^3 + y^3+ x\frac{dy}{dx}+ y =0\] now you can do the d/dx of y^3 , right ?

  15. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes.

  16. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    use the power rule \[ \frac{d y^n}{dx} = n y^{n-1} \frac{dy}{dx} \]

  17. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this isn't applying chain rule or is it? because i understand what youre doing here makes sense/

  18. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, it is the chain rule

  19. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    normally you do d/dx of x^3 and you get 3x^2 dx/dx but the dx/dx is left off and the rule looks like \[ \frac{d\ x^3}{dx} = 3 x^2 \]

  20. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay, let me give this a try.

  21. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay I got this down: x*3y^2(dy/dx) +3y +x(dy/dx)+y=0

  22. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you mean y^3 not 3y , right ?

  23. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh so only find the derivative of [y^3]...

  24. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks btw! :)

  25. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then i should just plot the points for x and y

  26. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wait a min. what should i do with dy/dx?

  27. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    solve for dy/dx and then sub in for x and y to get the value of dy/dx at the point (2,1)

  28. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how?

  29. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    use algebra

  30. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    question: is it possible to divide this: -4x/-2y ????

  31. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how the hell can someone divide this and get 2x/y?????

  32. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this is so frustrating, please help me understand this.

  33. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @asnaseer

  34. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what part is confusing ? you have \[3 x y^2\frac{dy}{dx} + y^3+ x\frac{dy}{dx}+ y =0 \] plug in x=2 and y =1 and solve for dy/dx (which is the slope)

  35. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    at the point (2,1)

  36. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no no, i know that. i was just looking at an example and i see that they divide -4x/-2y and got 2x/y

  37. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    it frustrated me to see this and not know how they even possibly do it.

  38. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    are you asking how to get from \[ \frac{-4x}{-2y} = \frac{2x}{y} \] ? -4/-2 is +2

  39. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes but with diferet variables?? 0.o

  40. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    different*

  41. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is the question ?

  42. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh the slope is -1/4! =]

  43. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes. also, the tangent line goes through point (2,1) so you can find the intercept.

  44. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    cool, how do you know this?

  45. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okie doke

  46. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks @phi you helped me so much! ^_^ so thankful

  47. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    they asked you to find the tangent line through point (2,1) you found its slope = -1/4 you know it goes through 2,1 so in point-slope form you have y- 1 = (-1/4)(x-2) which you can change to slope-intercept form

  48. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y=-1/4x+3/2

  49. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  50. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.