differential calculus question

** The symbol ' means d/dx **

(1)
y = (ax^2 + b)^3
y' = 3(ax^2 +b)^2 * (ax^2+b) '
= 3(ax^2 +b)^2 * (2ax)
=6ax(ax^2+b)^2

(2)
y = (x^3 + x)^7
y' = 7(x^3 +x)^6 * (x^3+x) '
= 7(x^3 +x)^6 * (3x^2+1)
= 7 (3x^2+1) (x^3 +x)^6

(3)
y = sqrt (x^2 +1) = (x^2+1)^(1/2)
y' = (1/2) (x^2+1)^(-1/2) * (x^2+1) '
= (1/2) (x^2+1)^(-1/2) * (2x)
= x (x^2+1)^(-1/2)
= x / sqrt (x^2+1)

You should keep practice using the chain rule until you do not need to use substitution.