Product of function and its derivative

[RasmusJes]

Hi there

Can someone please explain me this step when rewriting the Darcy equation?

q = -K*h*dh/dx = -0.5*K*d(h^2)/dx

I don't understand how h*dh/dx changes to 0.5*d(h^2)/dxThank you.

-Rasmus

 

[RasmusJes]

I have tried to separate variables, integrate on both sides, and then differentiate with regard to x:

q = -K*h*dh/dx
<=>
q dx = -K*h*dh
<=>
int q dx = int -K*h*dh
<=>
q*x = -0.5*K*h^2
<=>
d/dx q*x = d/dx (-0.5*K*h^2)
<=>
q = -0.5*K*d(h^2)/dx

Is that correct?

 

[Mute]

It's just recognizing the chain rule and reversing it:

\frac{dy^2(x)}{dx} = 2y(x)\frac{dy(x)}{dx}

 

[RasmusJes]

Wow, that took me a long time to understand :-) Thank you.
Would my suggestion, though much more awkward, still be right?