Question

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

Answer 1

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"

Answer 2

Sorry i meant x arrsin x.

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

Answer 3

xarcsinx*

Answer 4

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

Answer 5

*use the quotient rule

Answer 6

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

Answer 7

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