Answer
$4$ unit/sec
Work Step by Step
Step 1. Identify the given conditions: $y=x^{3/2}, s'=\frac{ds}{dt}=11u/sec, x=3$
Step 2. Calculate the distances: $y=(3)^{3/2}=3\sqrt 3, s=\sqrt {3^2+27}=6$, the point is $(3,3\sqrt 3)$
Step 3. Take derivative: $y=x^{3/2}$, $y'=\frac{3}{2}x^{1/2}x'=\frac{3}{2}\sqrt 3x'=$
Step 4. Take derivatives: $s^2=x^2+y^2$, $2ss'=2xx'+2yy'$ or $ss'=xx'+yy'$
Step 5. Plug-in the known numbers: $6(11)=3x'+3\sqrt 3(\frac{3}{2}\sqrt 3)x=3x'+27x'/2=33x'/2$
Thus $\frac{dx}{dt}=x'=4$ unit/sec
