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!

Homework Help: Chain Rule Question

  1. Nov 4, 2004 #1
    Hey whats up,
    I had a question on the chain rule....How would I use the chain rule on a quotient...like if i have 1/(t^4 + 1)^3 , Would I use the quotient rule first, or just start with the chain rule?
  2. jcsd
  3. Nov 5, 2004 #2
    ok use the chain rule SO:

    (bottom*d of top - top (d of bottom) )/bottom squared

    wen u do all that u get (i may be wrong though)

    -12t^3/(t^4 +1)^4
  4. Nov 5, 2004 #3
    there are many rules u can use

    like i used the quotient rule there
    u can also solve it by using the prduct rule (WHICH I GOT WRONG ON THE TEST ERRR)
  5. Nov 5, 2004 #4
    cool..thanks man.
  6. Nov 5, 2004 #5
    Either one works.

    Quotient rule:

    [tex]f(t) = \frac{p(t)}{q(t)} = \frac{1}{(t^4 + 1)^3}[/tex]
    [tex]p(t) = 1[/tex]
    [tex]q(t) = (t^4+1)^3[/tex]
    which are both functions of t.

    Alternatively, the chain rule:

    [tex]f(t) = f(u(t)) = \frac{1}{u^3}[/tex]
    where [itex]u(t) = t^4 + 1[/itex]

    So we have

    [tex]\frac{d}{dt}f(u(t)) = \frac{df}{du}\frac{du}{dt}[/tex]
    [tex] = \frac{d}{du}\left( u^{-3} \right) \frac{d}{dt}\left( t^4 + 1 \right) = (-3u^{-4})\cdot (4t^3) = \frac{-12t^3}{(t^4+1)^4}[/tex]

    I imagine the chain rule method is a bit faster, and I personally think I'd be more likely to make a silly mistake with the quotient rule, so.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook