is the product of the Jacobians of
its component transforms.</p>
<p>First, for the inverse transform <span class="math inline">\(z = \tanh y\)</span>, the derivative is</p>
<p><span class="math display">\[
\frac{d}{dy} \tanh y = \frac{1}{(\cosh y)^2}.
\]</span></p>
<p>Second, for the inverse transform of <span class="math inline">\(z\)</span> to <span class="math inline">\(x\)</span>, the resulting
Jacobian matrix <span class="math inline">\(J\)</span> is of dimension <span class="math inline">\(\binom{K}{2