#### Answer

$$g'(u)=4[(u^2-1)^6-3u]^3(12u(u^2-1)^5-3)$$

#### Work Step by Step

$$g'(u)=\left([(u^2-1)^6-3u]^4\right)'=4[(u^2-1)^6-3u]^3((u^2-1)^6-3u)'=
4[(u^2-1)^6-3u]^3(6(u^2-1)^5(u^2-1)'-3)=
4[(u^2-1)^6-3u]^3(6(u^2-1)^5\cdot2u-3)=4[(u^2-1)^6-3u]^3(12u(u^2-1)^5-3)$$