The definition
Scap = mu3(s,k)/mu2(s,k)^3/2
is procedural not symbolic. The current values of mu3(s,k) and mu2(s,k) are fetched and substituted, giving the expression you see, which is a direct function of s that has no "memory" of being formed by mu3 and mu2 .
If you want explicit chain rule in terms of mu2 and mu3, then you need to define Scap first in terms of mu2 and mu3 and do the differentiation before you give the formula for mu2 and mu3.
syms s k mu2(s,k) mu3(s,k) mu4(s,k) Scap(s,k)
Scap = mu3(s,k)/mu2(s,k)^3/2;
dScap = diff(Scap(s,k),s)
mu2(s, k) = 1 + 6*k^2 - 24*k*s^2 + 25*s^4;
mu3(s,k) = 108*k^2*s - 468*k*s^3 + 36*k*s + 510*s^5 - 76*s^3 + 6*s;
subs(dScap)
Best Answer