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 calculus, derivatives

  1. Feb 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Find f'(x)= 16x - x-2 using first principles.

    2. Relevant equations
    x
    http://img153.imageshack.us/img153/8403/597137697c1f605c7a43d34qz4.png [Broken]


    3. The attempt at a solution
    I used dy/dx and got 2x-3 + 16 but I get something different when I use the formular I attempted several times and I cant get the same answer as the dy/dx.
    Please need help!!!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 20, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Do you mean "find f'(x) if f(x)= 16x- x-1"? That's quite different from what you say!

    If f(x)= 16x- x-2, then f(x+h)= 16(x+h)- (x+ h)-2

    f(x+h)- f(x)= 16(x+ h)- 16x - (x+h)-2+ x-2

    The first part of that is just 16x+ 16h- 16x= 16h.

    The second part is
    [tex]-\frac{1}{(x+h)^2}+ \frac{1}{x^2}[/tex]
    [tex]= \frac{-x^2}{x^2(x+h)^2}+ \frac{(x+h)^2}{x^2(x+h)^2}[/tex]
    [tex]= \frac{-x^2+ x^2+ 2hx+h^2}{x^2(x+h)^2}= \frac{2hx+ h^2}{x^2(x+h)^2}[/tex]
    so
    [tex]f(x+h)- f(x)= 16h+ \frac{2hx+h^2}{x^2(x+h)^2}[/tex]
    Now, what is (f(x+h)- f(x))/h and what is the limit of that as h goes to 0.
     
  4. Feb 21, 2009 #3
    Last edited by a moderator: May 4, 2017
  5. Feb 21, 2009 #4

    lanedance

    User Avatar
    Homework Helper

    you've lost a square from the denominator for no reason during your calc, they should work
     
  6. Feb 21, 2009 #5
    Thanks sorry about that it works perfectly!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differential calculus, derivatives
  1. Differential Calculus (Replies: 10)

  2. Differential calculus (Replies: 2)

Loading...