Assuming I have $u=z*h$ and $z^2=k*x$
How can I convert
$\frac{\mathrm{d} h}{\mathrm{d} x}->\frac{\mathrm{d} u}{\mathrm{d} z}$
I am convinced it involves using the chain rule. But I am unsure how I plug these in?
Am I supposed to do it like this?
$\frac{\mathrm{d} D}{\mathrm{d} x}=\frac{\mathrm{d} D}{\mathrm{d} z}*\frac{\mathrm{d} z}{\mathrm{d} x} = \frac{k}{2\sqrt{kx}}$
$\frac{\mathrm{d} h}{\mathrm{d} x}=\frac{\mathrm{d} h}{\mathrm{d} u}*\frac{\mathrm{d} u}{\mathrm{d} z}*\frac{\mathrm{d} z}{\mathrm{d} x}=\frac{kuh}{2z\sqrt{kx}}$
$\frac{\mathrm{d}^2 h}{\mathrm{d} x^2}=\frac{\mathrm{d} }{\mathrm{d} x}*\frac{\mathrm{d} h}{\mathrm{d} x}=\frac{k}{2\sqrt{kx}}$
$\frac{\mathrm{d} b}{\mathrm{d} x}=\frac{\mathrm{d} b}{\mathrm{d} z}*\frac{\mathrm{d} z}{\mathrm{d} x}=\frac{3k^2uh}{4z(kx)^{3/2}}$
Also once I have a solution in terms of x and h, and I don't know how to plug it back into my general equation to get $du/dz$