1. Not finding help here? Sign up for a free 30min 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!

Find the 2nd Derivative - Basic Calc

  1. Oct 8, 2009 #1
    1. The problem statement, all variables and given/known data

    If g is a twice differentiable function and f(x) = xg(x^2), find f" in terms of g, g', and g".


    2. Relevant equations



    3. The attempt at a solution

    I tried this with a lot of work, wouldn't be bothered to put it all here, and came up with:

    f'' = (6x)*g'(x^2) + (4x^3)*g"(x^2)

    Is this right or am I completely off? This question was confusing...

    Is this even what they're asking for?

    -Bob
     
  2. jcsd
  3. Oct 8, 2009 #2

    Avodyne

    User Avatar
    Science Advisor

    Your answer is correct! Getting it involves repeated use of the chain rule and the product rule.
     
  4. Oct 8, 2009 #3
    Thanks!

    I thought it looked like a weird answer so wasn't entirely sure.

    Gracias,
    Bob
     
  5. Oct 8, 2009 #4
    Yup, you are correct! I got: 4*x^3*g''(x^2)+6*x*g'(x^2).

    As Avodyne said, "Getting it involves repeated use of the chain rule and the product rule."

    So, you've just showed that you understand both of these concepts well!

    Solve in terms, generally means solve the equation/formula with y on one side and x on the other side.... So, you are making x independent of your equation/formula with y being dependent on x. IE: Think of the cartesian plane, (x,y) {(1,1), (2,2), (3,3), etc...}

    Sincerely,

    NastyAccident
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find the 2nd Derivative - Basic Calc
  1. 2nd derivative (Replies: 1)

  2. 2nd derivatives (Replies: 4)

Loading...