Find the derivative g (x) = ln (2x^2+1)

4x / (2x^2+1)

Step-by-step explanation:

g (x) = ln (2x^2+1)

Using u substitution

u = 2x^2 + 1

du = 4x dx

g' (x) = d/du (g (u) du)

We know that the derivative of ln (u) = 1/u since this is always positive

= 1 / u * du

Substituting x back into the equation

g' (x) = 1 / (2x^2+1) * 4x

= 4x / (2x^2+1)