Note:- 1) if y = x^n ; then dy/dx = n*x^(n-1)
Thus,
If y = (1+4x)^(1/3) ; then
Let f(x) = x^(1/3)...........(1)
And g(x) = (1+4x).........(2)
Thus, f(g(x)) = (1+4x)^(1/3) .................Answer
Now, dy/dx = y' = (1/3)*{(1 + 4x)^(-2/3)}*4
or, dy/dx = (4/3)*[(1+4x)^(-2/3)]