When simpver = NULL, the first-order derivative of
the explicit Preston equation at a given x-value is selected:
$$ f(x)=\frac{b\left[a^{4}\,c_{1}+a^{3}\left(2\,c_{2}-1\right)x+
a^2\left(3\,c_{3}-2\,c_{1}\right)x^{2}-3\,a\,c_{2}x^3-4\,c_{3}\,x^{4}\right]}{a^4\sqrt{a^2-x^2}}, $$
where P has five parameters: \(a\), \(b\), \(c_{1}\), \(c_{2}\), and \(c_{3}\).
\(\quad\) When simpver = 1, the first-order derivative of the simplified version 1 is selected:
$$ f(x)=\frac{b\left[a^{4}\,c_{1}+a^{3}\left(2\,c_{2}-1\right)x-
2\,a^2\,c_{1}\,x^{2}-3\,a\,c_{2}x^3\right]}{a^4\sqrt{a^2-x^2}}, $$
where P has four parameters: \(a\), \(b\), \(c_{1}\), and \(c_{2}\).
\(\quad\) When simpver = 2, the first-order derivative of the simplified version 2 is selected:
$$ f(x)=\frac{b\left[a^{4}\,c_{1}-a^{3}\,x-
2\,a^2\,c_{1}\,x^{2}\right]}{a^4\sqrt{a^2-x^2}}, $$
where P has three parameters: \(a\), \(b\), and \(c_{1}\).
\(\quad\) When simpver = 3, the first-order derivative of the simplified version 3 is selected:
$$ f(x)=\frac{b\left[a^{3}\left(2\,c_{2}-1\right)x-3\,a\,c_{2}x^3\right]}{a^4\sqrt{a^2-x^2}}, $$
where P has three parameters: \(a\), \(b\), and \(c_{2}\).