I am following a quantum mechanics text book which uses a simple looking substitution in a derivative.
The substitution is $\xi=\gamma x\tag1$
It then says that $\frac{d\psi}{dx}=\frac{d\psi}{d\xi}\frac{d\xi}{dx}=\gamma\frac{d\psi}{d\xi}\tag2$
So far so good. Now comes the part I don't follow. It says: $\frac{d^2\psi}{dx^2}=\gamma^2\frac{d^2\psi}{d\xi^2}\tag3$
I don't know how they get this. I tried $\frac{d^2\psi}{dx^2}=\frac{d^2\psi}{d\xi^2}\frac{d^2\xi}{dx^2}\tag4$ but I get $\frac{d^2\xi}{dx^2}=0$ by using the substitution in equation (1). I'd appreciate it if someone could explain this to me.
Another thing I tried is (suggested by comment below): $\frac{d}{dx}\left(\frac{d\psi}{dx}\right)=\frac{d}{dx}\left(\frac{d\psi}{d\xi}\frac{d\xi}{dx}\right)=\frac{d^2\psi}{dxd\xi}\frac{d\xi}{dx}+\frac{d\psi}{d\xi}\frac{d^2\xi}{dx^2}\tag5$
Now since $\frac{d^2\xi}{dx^2}=0$ equation (5) reduces to:$\frac{d}{dx}\left(\frac{d\psi}{dx}\right)=\frac{d}{dx}\left(\frac{d\psi}{d\xi}\frac{d\xi}{dx}\right)=\gamma\frac{d^2\psi}{dxd\xi}$
Once again, I'm stuck..