Chain Rule - In order to differentiate a function of a function, say #y, =f(g(x))#, where we have to find #(dy)/(dx)#, we need to do (a) substitute #u=g(x)#, which gives us #y=f(u)#. Then we need to use a formula called Chain Rule, which states that #(dy)/(dx)=(dy)/(du)xx(du)/(dx)#. In fact if we have something like #y=f(g(h(x)))#, we can have #(dy)/(dx)=(dy)/(df)xx(df)/(dg)xx(dg)/(dh)#
Here we have #y=(3x^2+1)^4# or say #y=(f(x))^4# and #(dy)/(df)=4(f(x))^3#
where #f(x)=3x^2+1# and #(df)/(dx)=3*2x=6x#
Hence #(dy)/(dx)=(dy)/(df)xx(df)/(dx)#
= #4(f(x))^3xx6x#
= #24x(3x^2+1)^3#
