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Math Help - Implicit diff first or inverse trig first?

  1. #1
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    Implicit diff first or inverse trig first?

    I am trying to diff wrt the following

    A*arcsin(tan(3xy)+2)

    where A is a contstant.

    Can anybody help?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ryanfoster View Post
    I am trying to diff wrt the following

    A*arcsin(tan(3xy)+2)

    where A is a contstant.

    Can anybody help?
    You are leaving us with a bit more guess work to do than I like.

    What do you want to differentiate, and with respect to what?

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    You are leaving us with a bit more guess work to do than I like.

    What do you want to differentiate, and with respect to what?

    RonL
    I would like to differentiate implicitly wrt to x :

    y=arcsin(tan(3xy)+2)

    Sorry about the lack of info - just getting back into mathematics after a 10 year gap
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  4. #4
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    Quote Originally Posted by ryanfoster View Post
    I would like to differentiate implicitly wrt to x :

    y=arcsin(tan(3xy)+2)

    Sorry about the lack of info - just getting back into mathematics after a 10 year gap
    Chain rule:
    y=asn(tan(3xy)+2)

    \frac{dy}{dx} = \frac{1}{\sqrt{1 - (tan(3xy) + 2)^2}} \cdot (tan^2(3xy) + 1) \cdot \left (3y + 3x \frac{dy}{dx} \right )

    Now solve for \frac{dy}{dx}

    -Dan
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