Determining $\frac{d^2\arcsin(2x)}{dx^2}$ I am hitting my head against a wall trying to understand how to differentiate this. 
$$f(x) = \frac{d^2\arcsin(2x)}{dx^2}$$
Can someone please hold my hand through this?  I understand that $\arcsin(2x) = \sin^{-1}(2x)$. 
Is this implicit differentiation?

Let $y=\arcsin(2x)$.  Then
$$2x=\sin y\tag1$$
and implicit differentiation with respect to $x$ gives
$$2=(\cos y)\frac{dy}{dx}\ .\tag2$$
Differentiating again,
$$0=(\cos y)\frac{d^2y}{dx^2}-(\sin y)\Bigl(\frac{dy}{dx}\Bigr)^2\ .\tag3$$
You can now use $(3)$ to get a formula for $\frac{d^2y}{dx^2}$ in terms of $y$ and $\frac{dy}{dx}$; use $(2)$ to eliminate $\frac{dy}{dx}$; and use $(1)$ to eliminate $y$, giving an answer in terms of $x$.
Good luck!
