(a)[2]
Find a formula for $\frac{dy}{dx}$.
(b)[2]
Show that the $x$-coordinate of $M$ obeys the equation $x = \frac{x + 3}{\ln(2x + 1)} - 0.5$.
(c)[2]
Show by calculation that the $x$-coordinate of $M$ is between $2.5$ and $3.0$.
(d)[3]
Use an iterative formula based on the equation in part (b) to find the $x$-coordinate of $M$ correct to $4$ significant figures. Give the result of each iteration to $6$ significant figures.