Finding d²z/dx² from a complex first derivative

[NouvaNouca]

Homework Statement

Knowing that:

$$\frac{dz}{dx}$$=$$\sqrt{\frac{(-T)^2}{(k*(z-a)*(z-2*b+a)/2-T*cos(phi))^2}-1}$$

What is:
$$\frac{d^2z}{dx^2}$$ ?

Homework Equations

I'm trying to solve using this general equation I found on Wikipedia (http://en.wikipedia.org/wiki/Differential_equation):

$$\frac{d^2z}{dx^2}$$ =F(z) when x= integral(1/$${\sqrt{\int F(z)*dz + C1}}$$,z)

The Attempt at a Solution

I've actually spent a couple of hours trying to solve this, but I can't find a way to solve for C1. Of course that if it's possible to solve this problem without using the general equation I propose well that's even better! Any help or comments would be greatly appreciated. Sorry that I couldn't make the equations look perfect using Latex, I hope they are clear enough.

 

[phyzguy]

Since you know:
$$\frac{dz}{dx} = f(z)$$
Just differentate again:
$$\frac{d^2z}{dx^2} = \frac{d}{dx}f(z) = \frac{df}{dz} \frac{dz}{dx} = f \frac{df}{dz}$$
So just differentiate the right hand side(which is f(z)) with respect to z, and multiply by f(z).