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=cos(6x^2)# i.e. #y=cos(g(x))#, where #g(x)=6x^2#
Hence #(dy)/(dx)=d/(dg(x))cos(g(x))xxd/(dx)6x^2#
= #-sin(6x^2)xx12x#
= #-12xcos6x^2#
