1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Implicit Differentiation.

  1. Oct 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Determine y'' when 5x^2 + 3y^2 = 4.



    3. The attempt at a solution

    So I found the first derivative using the power rule and chain rule,

    10x + 6yy' = 0

    Which I then solved for y',

    y' = -10x/6y = -5x/3y

    Next I found the second derivative using quotient rule,

    y'' = (-15y + 15xy')/(3y)^2

    This is the part where I am lost, since all the multiple choice answers involve no y' nor is there a x.
    I don't know how to get rid of the x and the y' in the equation. Any help will be appreciated as to simplifying the equation even further and as to how.
     
  2. jcsd
  3. Oct 5, 2013 #2

    statdad

    User Avatar
    Homework Helper

    Substitute the form of y' you have into the expression for y'' and simplify.
     
  4. Oct 5, 2013 #3
    Thanks statdad!

    so here's what I did,

    I substituted y' with -5x/3y and got

    y'' = (-15y + 15x(-5x/3y))/(3y)^2 = (-15y - 25x^2/y)/(3y)^2 = (-15y^2/y - 25x^2/y)/(9y^2) = (-15y^2-25x^2)/9y^3

    But I still had to get rid of the x, so I used the original equation to solve for x^2, which was;

    x^2 = (4-3y^2)/5

    Which I then use to simplify even further,

    y'' = (-15y^2 - 25((4 - 3y^2)/5))/9y^3 = ((-75y^2 - 100 + 75y)/5)/9y^3

    In which the answer is -20/9y^3.

    Thanks for the insight. For some reason I didn't see that.
     
  5. Oct 5, 2013 #4

    statdad

    User Avatar
    Homework Helper

    You are welcome. The little bit of ``extra'' work you've just gone through is handy to remember for these types of problems - I would state with near 100% certainty you'll see similar things in the future.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Implicit Differentiation.
Loading...