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Math Help - Differentiation help

  1. #1
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    Differentiation help

    Prove that \frac{d}{dx} \arcsin x=\frac{1}{\sqrt{1-x^2}}
    Given that the variables x and y satisfy the equation
    \arcsin 2x+\arcsin y+\arcsin (xy)=0
    find \frac{dy}{dx} when x=y=0

    I have done the first part, proving \frac{d}{dx} \arcsin x=\frac{1}{\sqrt{1-x^2}}.
    I don't know how to do this second part. Differentiating arcsinx I know how, but arcsiny and arcsin(xy) I don't know what to do. Any pointers?
    Thanks
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  2. #2
    Senior Member nikhil's Avatar
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    1) d(arcsin(y))/dx= 1/sqrt[1-y^2] (dy/dx)
    2) d(arcsin(xy))/dx= 1/sqrt[1-(xy)^2] (d(xy)/dx)
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  3. #3
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    Thanks! how could i have forgotten that
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  4. #4
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    err, i'm supposed to find dy/dx, what do i do with d(xy)/dx?
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  5. #5
    Senior Member nikhil's Avatar
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    d(xy)/dx =(y+x dy/dx)
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