... angle 1
k = x²+1
dk/dx = 2x
dk = 2xdx
y = (x²+1)³ = k³
dy/dk = 3k²
dy/2xdx = 3k²
dy/dx = 2x(3k²) = 6x(x²+1)²
... angel 2
dy/dx = d[(x²+1)³]/dx
= { d[(x²+1)³]/dx }(d(x²+1) / d(x²+1))
= { d[(x²+1)³]/d(x²+1) }(d(x²+1) / dx )
= { 3(x²+1)² }(2x) = 6x(x²+1)²
