Results 1 to 3 of 3

Math Help - A couple of basic calculus problems

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    32

    A couple of basic calculus problems

    Hello,

    Could I get a hint about how to deal with a couple of calculus problems:

    1) The integral of Sec^2(3x)

    2) The derivative of y + 2xSin(y) = e^x (i.e. dy/dx)

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Just in case a picture helps...



    ... where (key in spoiler)...

    Spoiler:


    ... is the chain rule, here embedded in the legs-uncrossed version of...



    ... the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).


    Spoiler:


    And here, to integrate and therefore travelling up instead of down,



    ... you're meant to integrate sec^2 as a standard integral (but see here).

    Spoiler:

    __________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; September 22nd 2010 at 01:58 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    Quote Originally Posted by DangerousDave View Post
    Hello,

    Could I get a hint about how to deal with a couple of calculus problems:

    1) The integral of Sec^2(3x)
    You are expected to know that the derivative of tan(x) is sec^2(x).

    2) The derivative of y + 2xSin(y) = e^x (i.e. dy/dx)
    Do you know "implicit differentiation"? What is the derivative of sin(y) with respect to x? What is the derivative of 2x sin(y) with respect to x?

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. More basic topology (couple questions)
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 4th 2011, 09:19 AM
  2. A few basic calculus derivative problems
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 3rd 2010, 02:34 PM
  3. Couple of Calculus Problems
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 18th 2010, 06:35 PM
  4. Couple of basic chemistry questions
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: June 5th 2007, 04:03 PM
  5. basic calculus problems
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 18th 2007, 02:31 PM

Search Tags


/mathhelpforum @mathhelpforum