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Math Help - A little stuck on a derivative

  1. #1
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    A little stuck on a derivative

    i was trying to differentiate h(x) = (1-x^(2))^(1/2) * arcsin(x^(2))

    I came up with (2x^(2))/[((1-x^(2))^(1/2)) * ((1-x^(4))^(1/2))]

    can that be simplified further? My algebra is a little rusty... Thanks for your time.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by drain View Post
    i was trying to differentiate h(x) = (1-x^(2))^(1/2) * arcsin(x^(2))

    I came up with (2x^(2))/[((1-x^(2))^(1/2)) * ((1-x^(4))^(1/2))]

    can that be simplified further? My algebra is a little rusty... Thanks for your time.
    Why is there no arcsin in you derivative?

    The attachment shows QuickMath's answer.

    RonL
    Attached Thumbnails Attached Thumbnails A little stuck on a derivative-gash.jpg  
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  3. #3
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    Hello, drain!

    Product rule?


    Differentiate: .h(x) .= .(1 - x)^ arcsin(x)

    . . . . . . . . . . . . . . . . . . .2x
    h'(x) . = . (1 - x)^ ----------- .+ .(1 - x)^{-)(-2x) arcsin(x)
    . . . . . . . . . . . . . . . . √1 - x^4


    It doesn't simplify very much . . .
    . . . . . . . . . . _____
    . . . . . . . .2x√1 - x . . .xarcsin(x)
    h'(x) . = . ------------ .- .--------------
    . . . . . . . √1 - x^4 . . . . 2√1 - x

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Hmmm . . .
    . . . . . . . . . . . . . . . . . . . . . . . .2x
    The first fraction reduces to: . -----------
    . . . . . . . . . . . . . . . . . . . . . .√1 + x

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  4. #4
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    Thanks to both of you very much! Guess I still need some practice on these And thanks for the quickmath site! Good way to check my work =)
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