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Differntiating inverse trigonometric functions

  • 06-05-2012 4:58pm
    #1
    Chuchoter
    Registered Users, Registered Users 2 Posts: 4,305 ✭✭✭


    I can do these when its a constant on the bottom as I can find examples of sin^-1 (x/a), but how do you do the ones where its got an x on the bottom? Like tan^-1(2x/x+5) for example? I've seen ones where you multiply by the differentiate but they seem very messy.


Comments

  • #2
    finality
    Registered Users, Registered Users 2 Posts: 1,763 ✭✭✭finality


    Think of it as (2x/x+5)/1

    2x/x + 5 is x in the tables
    and 1 is a


  • #3
    Chuchoter
    Registered Users, Registered Users 2 Posts: 4,305 ✭✭✭Chuchoter


    Thank you!


  • #4
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    Don't forget that you'll also need to multiply by the derivative of what's in thebrackets, (as it's a chain rule).


  • #5
    unmoeglichkeit
    Registered Users, Registered Users 2 Posts: 13 ✭unmoeglichkeit


    You could always differentiate implicitly, just change the function to

    y= tan^-1(2x/x+5)
    tany=2x/x+5

    and then use implicit differentiation


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