Drone

A drone is programmed to fly in a pattern where the function gives its vertical displacement $($in meters$)$ from a base station:

$v(t)=sin(\frac{t}{\sqrt[\phantom{2}]{t1}})$

where is the time in seconds after take$-$off. An engineer wants to understand how fast the vertical position is changing at specific times during the flight in order to adjust the drone's stability system.a$.$ Calculate the rate of change of vertical position at $t=3$ seconds. Round your answer to $3$ decimal places.

$(5$ Marks$)$

b$.$ Explain what this rate means in the context of the drone's motion.

$(2$ Marks$)$

c$.$ At what time will the drone momentarily stop ascending or descending?

$(5$ Marks$)$

$6\mathrm{.}2$ Calculate $f^{\text{'}}(1)$ if $f(x)=\frac{x^{2}lnx}{3x^3-1}.$

$($$ Marks$)$