Results 1 to 3 of 3

Math Help - inverse function differentiation

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    39

    inverse function differentiation

    Let
    F(x) = \int_{1}^{x}{(1+t^2)^{\frac{1}{2}}dt} , 1 \le x . Let G be the inverse function of F. Evaluate G'(0).

    I have F'(x)=(1+x^2)^{\frac{1}{2}} for 1 \le x but I am having trouble finding G(x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by 234578 View Post
    Let
    F(x) = \int_{1}^{x}{(1+t^2)^{\frac{1}{2}}dt} , 1 \le x . Let G be the inverse function of F. Evaluate G'(0).

    I have F'(x)=(1+x^2)^{\frac{1}{2}} for 1 \le x but I am having trouble finding G(x)
    Dear 234578,

    Try integrating the expression and obtain F(x) using the substitution, t=tan\theta

    Afterwards you could find the inverse of F(x) and G'(0)

    Hope this will help you.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    Quote Originally Posted by 234578 View Post
    Let
    F(x) = \int_{1}^{x}{(1+t^2)^{\frac{1}{2}}dt} , 1 \le x . Let G be the inverse function of F. Evaluate G'(0).

    I have F'(x)=(1+x^2)^{\frac{1}{2}} for 1 \le x but I am having trouble finding G(x)
    since F and G are inverses ...

    F[G(x)] = x

    F'[G(x)] \cdot G'(x) = 1

    G'(x) = \frac{1}{F'[G(x)]}

    G'(0) = \frac{1}{F'[G(0)]}

    since F(1) = 0 , G(0) = 1

    G'(0) = \frac{1}{F'(1)}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Inverse and Differentiation
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: June 15th 2011, 04:14 AM
  2. Differentiation of inverse tanh
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 16th 2010, 07:42 PM
  3. Replies: 2
    Last Post: July 17th 2009, 07:41 PM
  4. Differentiation of Inverse Trig Function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 15th 2008, 05:03 AM
  5. inverse trigonometric differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 8th 2006, 05:06 PM

Search Tags


/mathhelpforum @mathhelpforum