Posted by **anon** on Monday, October 21, 2013 at 5:54pm.

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

- math -
**Steve**, Monday, October 21, 2013 at 6:50pm
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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**anon**, Monday, October 21, 2013 at 7:34pm
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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**anon**, Monday, October 21, 2013 at 7:35pm
xarcsinx*

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**anon**, Monday, October 21, 2013 at 7:37pm
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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**anon**, Monday, October 21, 2013 at 7:38pm
*use the quotient rule

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**anon**, Monday, October 21, 2013 at 7:52pm
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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**anon**, Monday, October 21, 2013 at 8:11pm
please help me. I don't know what I am doing wrong

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