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Math Help - Differentiate

  1. #1
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    Post Differentiate

    Hey all on mhf,

    Im stuck on a this question and needed some help please.


    Differentiate:

    x\sqrt{1-x^2}-sin^{-1}\sqrt{1-x^2}


    Oh dear the LaTex is still not enabled.

    I hope you can still see what the question is, Thank you.
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  2. #2
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    Hello, dadon!

    Differentiate: .f(x) .= .x(1 - x)^ - arcsin(1 - x)^
    That arcsin expression is very messy to differentiate, so I modified it.

    We have: .θ .= .arcsin(1 - x)^ . . sin θ .= .(1 - x)^

    θ is an angle is a right triangle with: .opp = (1 - x)^ .and .hyp = 1.
    . . Pythagorus tell us that: .adj = x
    Hence: .cos θ = x . . θ = arccos(x)


    The function becomes: . f(x) .= .x(1 - x)^ - arccos(x)


    Then: . f'(x) .= .x(1 - x)^{-)(-2x) + (1 - x)^ + (1 - x)^{-)

    Rearrange: .(1 - x)^{-} - x(1 - x)^{-} + (1 - x)^

    Factor: . (1 - x)(1 - x)^{-} + (1 - x)^

    . . . . = .(1 - x)^ + (1 - x)^

    . . . . = .2(1 - x)^

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