A marine biologist models the rate of change of the depth of a diving seal, DDD (in metres), relative to time sss (in seconds) for s>0 s > 0\,s>0 using the following formula:
dDds=7s34−35s23+27 \frac{dD}{ds} = \frac{7s^3}{4} - \frac{3}{5\sqrt[3]{s^2}} + \frac{2}{7} dsdD=47s3−53s23+72Determine the general equation for the depth D D\,D in terms of sss, giving your answer in its simplest form.
