  We present scheme-independent calculations of the derivative of the beta
function, denoted $\beta'_{IR}$, at a conformally invariant infrared (IR) fixed
point, in several asymptotically free chiral gauge theories, namely SO($4k+2$)
with $2 \le k \le 4$ with respective numbers $N_f$ of fermions in the spinor
representation, and E$_6$ with fermions in the fundamental representation.
