Given: $y=\sqrt[\phantom{2}]{x}+2$

$5$ points each

a$)$ Find $d\frac{y}{d}x$

b$)$ Find $(d\frac{y}{d}x{)}^2$

c$)$ Find the arc length from $x=1$ to $x=4$ by setting up integral but use calculator to solve, round to $3$ decimals. ${?}^{******}$ Careful with parentheses on calculator

d$)$ Find the area of the surface generated by rotating the curve around the $x-$axis from $x=1$ to $x=4.$ Set up integral and use calculator to find the value. Round to $3$ decimals. ${?}^{******}$ Careful with parenthese on calculator