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!

Differential of a^x^b

  1. May 26, 2015 #1
    • Member warned about posting with no effort
    1. The problem statement, all variables and given/known data
    Find the differential of axb

    2. Relevant equations


    3. The attempt at a solution
    Really not sure where to start, honestly. Thanks in advance :)
     
  2. jcsd
  3. May 26, 2015 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Show some effort at understanding the problem.

    How does a person find a differential?
     
  4. May 26, 2015 #3
    In the picture is what I have so far.
    Not sure if correct or not.
     

    Attached Files:

  5. May 26, 2015 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    That's pretty difficult to read.

    It looks like you let ##\displaystyle\ y=a^{\displaystyle x^b}\,,\ ## then found the derivative, ##\displaystyle\ \frac{dy}{dx}\ ##.

    So, now to get the differential.
     
  6. May 26, 2015 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Perhaps he/she was being asked to find the derivative, but due to a language issue it came out as "differential".
     
  7. May 26, 2015 #6
    As I also thought they are similar (derivative and differential), or maybe I'm wrong...?
    It seems correct and I have a suggestion that you can differentiate on ##x## instead of ##y## while the process is similar (just a little easy).
     
  8. May 26, 2015 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes. That's an excellent point!

    When ninjaduck did implicit differentiation, he took the derivative with respect to y, rather than the customary method of taking the derivative with respect to x .
     
  9. May 27, 2015 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, if [itex]y= a^{x^b}[/itex] then [itex]\frac{dy}{dx}= ba^{x^b}ln(a)x^{b- 1}[/itex].

    You used "logarithmic differentiation". If you do that with just [itex]y= a^x[/itex] then [itex]ln(y)= x ln(a)[/itex] so that [itex]y'/y= ln(a)[/itex], [itex]y'= y ln(a)= ln(a) a^x[/itex]. I find it simpler to use that generally.

    Here, we use the chain rule with [itex]u(x)= x^b[/itex] so that [itex]y= a^u[/itex]. Then [itex]y'= ln(a) a^u (u')[/itex]. Since [itex]u= x^b[/itex], [itex]u'= bx^{b- 1}[/itex]. Putting those together, the derivative of [itex]y= a^{x^b}[/itex] is [itex]dy/dx= ln(a)\left(a^{x^b}\right)\left(bx^{b-1}\right)[/itex], just what you have.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Differential of a^x^b
  1. Differentiate x^(x^2) (Replies: 4)

  2. Grad x (grad x B) (Replies: 5)

Loading...