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!

Differentiate the function (derivatives, difference of sums rule)

  1. May 7, 2013 #1
    1. The problem statement, all variables and given/known data
    [itex] f(x) = x^{1/2} - x^{1/3} [/itex]

    2. Relevant equations
    [itex] f(x) = f'(x)- g'(x)[/itex]

    3. The attempt at a solution
    I am a little stuck about what to do after the first couple steps. Here is my attempt.

    [itex] f(x) = x^{1/2} - x^{1/3}[/itex]
    [itex]f'(x) = (x^{1/2})' -(x^{1/3})'[/itex]
    [itex]= 1/2x^{-1/2} - 1/3x^{-2/3}[/itex]
    **** this is where I get confused *****
    [itex]= 1/2x^{1/2} - 1/3x^{2/3}[/itex]
    [itex]= ?[/itex]

    Ps, I was recently told by a mentor not to write the prime in my solution, however, I'm leaving it like this because this is how it was taught in the course and I'm trying to avoid confusing myself further. Thank you.
  2. jcsd
  3. May 7, 2013 #2
    wat is confusing about it? you got the right answer halfway through. how would you write x^-1/2? remember that x1/2 is of course [itex]\sqrt[]{x}[/itex]. so x-1/2 would be 1 over that: 1/[itex]\sqrt[]{x}[/itex]. same concept remember with x-1 = 1/x.

    maybe the power of x is confusing you. remember that x3/4 for instance is the same as [itex]\sqrt[4]{x^3}[/itex].

    so you could also write it as 0.5/[itex]\sqrt[]{x}[/itex] - 0.333/[itex]\sqrt[3]{x^2}[/itex]
    Last edited: May 7, 2013
  4. May 7, 2013 #3
    Oh okay I think I understand. Thank you :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Differentiate function derivatives Date
Find the derivative of this function Jan 12, 2018
Finding dy/dx for a circle Jul 4, 2017
Differentiation with respect to a function May 8, 2015
Partial Differentiation -- y deleted or ignored? May 2, 2015
Functional Derivatives Jan 31, 2015