How do I evaluate: $$\nabla \cdot K(h)\frac{\partial h}{\partial z}$$
I am applying: $(fg)'=f'g+g'f$
and I am getting: $$\frac{K(h)}{dz}\frac{\partial h}{\partial z}+K(h)\frac{d^2h}{dz^2}$$ now comes the question, am I allowed to do that? $$\frac{K(h)}{dz}\frac{\partial h}{\partial z}+K(h)\frac{d^2h}{dz^2}=\frac{K(h)}{dz}\frac{\partial h}{\partial z}+\frac{K(h)}{dz}\frac{\partial h}{\partial z}$$ So that in the end: $$\nabla \cdot K(h)\frac{\partial h}{\partial z}=2\frac{K(h)}{dz}\frac{\partial h}{\partial z}\ ?$$
I am quite rusty in my Calculus ... sorry if the question seems trivial.
Thanks in advance for anwering!
Just to be clear, I am trying to compare the equation from Celia et. al, 1990 to Wikipedia (the original equation from Richards). The form by Richards seems to me like the mixed equation... I just don't know how they get it ... (To non hydrogeologists: $h=\psi + z$)