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 with respect to x

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Differentiate with respect to x

    y = tan^(-1) x



    2. Relevant equations



    3. The attempt at a solution

    ANSWER in book:

    y = tan^(-1) x
    x = tan y
    dx/dy = sec^(2) y = (1 + x^2)
    dy/dx = 1 / (1 + x^2)

    How is it known that sec^(2) y = (1 + x^2)
    Does it follow from an identity?
     
  2. jcsd
  3. Jan 16, 2012 #2
    Have this sorted.

    It follows from the identity sin^2 (x) + cos^2 (x) = 1
     
  4. Jan 16, 2012 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    It follows from
    x = tan(y)​
    So that
    tan2(y)=x2
    Then use the identity relating sec2 and tan2 , etc.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook