$2.(3$pts each part$)$ A manufacturer of calculators has determined that the revenue to produce $\backslash ($ x $\backslash )$ units per week is given by

$\backslash [$

R$=170$ x$-\backslash$frac$\{$x$^\{2\}\}\{53\}-40000$

$\backslash ]$

Answer the following questions:

a$)$ Implicitly differentiate the given function with respect to time $\backslash ($ t $\backslash ).$ You do not need to simplify.

b$)$ Suppose that production is changing at the rate of $21$ units per week when the production level is $5700$ units. How fast is the revenue per week changing at that moment? Leave your answer in math expression. Do not simplify.