Differentiate with respect to x: y = ln(x^2+4*x+2).

Let u = x²+4x+2 so y = ln(u).

Then dy/du = 1/u and du/dx = 2x+4.

Using the chain rule we have:

dy/dx = (dy/du)*(du/dx)

= (1/u)*(2x+4)

= (2x+4)/(x²+4x+2).