Results 1 to 3 of 3

Math Help - Simple trig differentiation

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    229

    Simple trig differentiation

    If f(x) = 8x arcsin x, find f'(x).

    I know that we have to apply the product rule, but something isn't adding up (no pun intended).

    My procedure;
    f'(x) = 8 (arcsin x) + 8x * 1 / (1+x^2)^2
    f'(x) = 8 arcsin x + 8x / (1+8x^2)^1/2

    What went wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Archduke01 View Post
    If f(x) = 8x arcsin x, find f'(x).

    I know that we have to apply the product rule, but something isn't adding up (no pun intended).

    My procedure;
    f'(x) = 8 (arcsin x) + 8x * 1 / (1+x^2)^2
    f'(x) = 8 arcsin x + 8x / (1+8x^2)^1/2

    What went wrong?
    \int\frac{dx}{\sqrt{1+x^2}}=\text{arcsinh}(x)...hint hint.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    104
    We know the derivative of arcsin (x)=1/sqrt(1-x^2).

    For the product rule, we want the FIRST times the derivative of the second PLUS the SECOND times the derivative of the first.

    Here, the first is 8x and the second is arcsin (x).

    I get f'(x)=(8x/sqrt(1-x^2))+8 arcsin (x)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple differentiation!
    Posted in the Calculus Forum
    Replies: 9
    Last Post: May 21st 2011, 12:24 PM
  2. Replies: 2
    Last Post: November 12th 2009, 04:09 PM
  3. Simple log differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 7th 2008, 03:40 PM
  4. Simple Differentiation..
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 2nd 2007, 07:50 PM
  5. differentiation of simple trig fuction
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 3rd 2007, 08:59 AM

Search Tags


/mathhelpforum @mathhelpforum