To differentiate #y=(x^4+3x^2-2)^5#, we use Chain Rule .
The concept under this rule is that of a function of a function, say #y, =f(g(x))#, where we have to find #(dy)/(dx)#. What we need to do is (a) to 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)#.
Here we have #y=f(g*x))=g(x)^5# where #g(x)=x^4+3x^2-2#
Hence, #(dy)/(dx)=d/(d(x^4+3x^2-2))(x^4+3x^2-2)^5xxd/(dx)(x^4+3x^2-2)#
= #5(x^4+3x^2-2)^4xx(4x^3+6x)#
= #10x(2x^2+3)(x^4+3x^2-2)#
