Posted by anon on .
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,
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,
Sorry i meant x arrsin x.
So I thought the first derivative of that would be
x/sqrt1x^2 + arcsinx 
math 
anon,
xarcsinx*

math 
anon,
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,
*use the quotient rule

math 
anon,
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,
please help me. I don't know what I am doing wrong