Lately i'm doing lot of research regarding procedural terrain generation. I do a lot of learning from www.iquilezles.org. I'm now familiar with such things as perlin/simplex noise, fbm, domain warping, etc. But right now I'm looking into this > https://www.iquilezles.org/www/articles/morenoise/morenoise.htm and am very clueless what are those derivatives, what do they represent and how to use them. Maybe someone can put this knowledge in more simple words or/and illustration? Thank you in advance.
The derivative of a function gives you the slope at each point of said function (it actually gives you the rate of change, but the two are identical for the first derivative)
For instance if you have the function \$f(x)=x\$, the derivative would be \$f'(x)=1\$, since the slope of the function is 1 at every point. Similarly for \$g(x)=x^2\$ it would be \$g'(x)=2x\$.
Knowing the slope of a function at any specific point is great, because it can be used to calculate the normals of the function, which can then be used to do lighting and other stuff, the article gives you a couple of ideas.
The second derivative is a bit harder to use in this context. It generally allows us to get the local minimums and maximums of any function by looking for coordinates where the second derivative is 0 and the signs of the values on the sides are different.