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
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"
Sorry i meant x arrsin x.
So I thought the first derivative of that would be
x/sqrt1-x^2 + arcsinx
xarcsinx*
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
*use the quotient rule
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