Suppose $f(x)=ln(x2+1)$

$($a$)$ Calculate the first and second derivatives of $f.$

$($b$)$ Determine the intervals where $f$ is increasing or decreasing.

$($c$)$ Determine all local maxima and minima for $f.$

$($d$)$ Determine the intervals where $f$ is concave up or concave down.

$($e$)$ Determine all points of inflection for $f.$

$($f$)$ Using $(1)-(5),$ and plotting two or three points on the graph, sketch a graph of $f.$