Given that \[y=x-\ln(1+x^2),\] show that \[\frac{dy}{dx}\geq 0\ \text{for all values of $x$.}\]

Deduce that, for all \(x>0\), \[x>\ln(1+x^2).\]

Given that \[y=x-\ln(1+x^2),\] show that \[\frac{dy}{dx}\geq 0\ \text{for all values of $x$.}\]

Deduce that, for all \(x>0\), \[x>\ln(1+x^2).\]