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 = 2x^2/(1x^2)^3/2

math  Steve, Monday, October 21, 2013 at 6:50pm
straightforward derivative. Where do you get stuck?
y' = (1x^2)^(1/2)
now just use the power rule and chain rule to get y"

math  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/sqrt1x^2 + arcsinx

math  anon, Monday, October 21, 2013 at 7:35pm
xarcsinx*

math  anon, Monday, October 21, 2013 at 7:37pm
I get stuck on the second derivative, trying to get it to equal 2x^2/(1x^2)^3/2.
I think that from my first derivative, you have to sure the quotient rule

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

math  anon, Monday, October 21, 2013 at 7:52pm
I tried to use the quotient rule but I get stuck simplifying it.
I got
(sqrt1x^2)(1/sqrt1x^2)  (x+arcsinx)(1/2(1x^2)2x) / (sqrt1x^2)^2

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