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!

How to find differencial by using implicit functions?

  1. Mar 18, 2013 #1
    1. The problem statement, all variables and given/known data
    R=1/(.55/c+.45/h)
    find partial equations respect to c. and respect to h
    use implicit function differentiation of the reciprocal of R to answer
    what is the differential change in R when c=20 h=30 and c changes to 21


    2. Relevant equations
    is there any way to make R easier?
    i said that R=ch/(.55h+.45c) which was the best i could do.
    Is there any other way to make R easier?

    3. The attempt at a solution
    i got the partial equations if the R=ch/(.55h+.45c) is right.
    but im not sure how to use implicit or what implicit is. i just found it normally.
    WHen it says what is the differential change in R when c=20 and h=3 and c changes to 21. do i just substitude them to the partial differentials and add them?
     
  2. jcsd
  3. Mar 18, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, R= ch/(.55h+ .45c) is correct and about as simple as it gets. I notice that the problem asks you to "use implicit function differentiation of the reciprocal of R. That is, of course, 0.55h+ 0.45c= chR. Differentiate both sides of that with respect to h to find [itex]\partial R/\partial h[/itex]. (Surely you remember "implicit differentiation" from Calculus I?)

    In general the "differential" of a function, f(h,c), is
    [tex]df= \frac{\partial f}{\partial h}dh+ \frac{\partial f}{\partial c}dc[/tex]

    But notice that, in this problem, only c changes.
     
  4. Mar 18, 2013 #3
    thank you.
    just one more thing.
    could you walk me through implicit differentiation on this problem?
    i start off when i find dR/dh. i got .55+0=crDr/dh ? is this right or am i missing something?
     
  5. Mar 18, 2013 #4
    Hello munkhuu, I believe this link would be tremendously helpful in solving your problem: http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx

    To use implicit differentiation, you need to first present the given equation in the form F(R,c,h) by isolating the three variables into one side. So in our case, F(R,c,h)=R-[itex]\frac{ch}{0.55h+0.45c}[/itex]=0. And according to the Implicit Differentiation Rule, ∂R/∂c=-(∂F/∂c)/(∂F/∂h) (notice the negative sign!!), where ∂F/∂c=[h*(0.55h+0.45c)-ch*(0.45)]/[0.55h+0.45c]^2 (using the quotient rule and considering h and R constants, we have differentiated F with respect to c); and ∂F/∂R=1. Proceed in a similar fashion and we will get ∂R/∂h.

    As for part b), in order to find the marginal effect of c on R (notice that h remains unchanged), we just need to multiply ∂R/∂c with ∂c to get rid of the denominator, and plug in (c=21, h-30, ∂c (change in c)=1). I hope my approach is right. Good luck :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted