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Let y = arcsin x, x is an element of ]-1, 1[. Show that d^2y/dx^2 = 2-x^2/(1-x^2)^3/2

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straightforward derivative. Where do you get stuck?

y' = (1-x^2)^(-1/2)
now just use the power rule and chain rule to get y"

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Sorry i meant x arrsin x.

So I thought the first derivative of that would be
x/sqrt1-x^2 + arcsinx

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xarcsinx*

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I get stuck on the second derivative, trying to get it to equal 2-x^2/(1-x^2)^3/2.

I think that from my first derivative, you have to sure the quotient rule

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*use the quotient rule

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I tried to use the quotient rule but I get stuck simplifying it.
I got

(sqrt1-x^2)(1/sqrt1-x^2) - (x+arcsinx)(1/2(1-x^2)2x) / (sqrt1-x^2)^2

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