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: Differentiating this

  1. Jun 7, 2006 #1


    User Avatar
    Gold Member

    Hey. If i have:
    y = 2x\sqrt {4 - 2x^3 }

    To differentiate it, i used the product rule, but used the chain rule to differentiate the [itex]\sqrt {4 - 2x^3}[/itex] part. I got the answer right, but was just wondering, is there a quicker way of doing it? Or have i gone about it the right way?

  2. jcsd
  3. Jun 7, 2006 #2


    User Avatar
    Homework Helper

    You've done it the right way :smile:
  4. Jun 7, 2006 #3
    As far as I know there is no othere way (execept if you use a computer). And it really isn't that long either.

    PS Somethimes it's easier if you differentiate using logoritems (especially if theres a lot of multiplication involved).
  5. Jun 7, 2006 #4


    User Avatar
    Science Advisor

    I'm not sure what you would consider 'quicker' but writing this as
    [tex]y= 2x(4- 2x^3)^\frac{1}{2}[/tex]
    at least makes the derivative a bit clearer.
  6. Jun 7, 2006 #5


    User Avatar
    Gold Member

    Yea thats what i did. Then i said that [tex]f(x)=2x[/tex] and [tex]g(x)=(4- 2x^3)^\frac{1}{2}[/tex]. I then differentiated g(x) with the chain rule, then once i found that, i used the product rule to find the final derivative.
  7. Jun 7, 2006 #6


    User Avatar
    Homework Helper

    Or you could do some algebra and throw the 2x into the square root before doing any calculus operations, which removes the need for the product rule.

    [tex]y = 2x \sqrt{4-2x^3} = \sqrt{4x^2 (4-2x^3)} [/tex]
  8. Jun 7, 2006 #7
    The above however doesn't work well, because you lose the sign.

    Another potential way to simplify might be to take logarithm and differentiate that, but you have to be careful there.
  9. Jun 7, 2006 #8


    User Avatar
    Gold Member

    I never thought of doing it like that :rolleyes:

    Thanks for the replies everyone.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook