Suppose that the total cost $($in dollars$)$ for a product is given by $C(x)=1200+190ln(3x+1)$ where $x$ is the number of units produced.

$($a$)$ Find the marginal cost function, $\frac{?}{\text{b}\text{a}\text{r}}(MC).$

$\frac{?}{\text{b}\text{a}\text{r}}(MC)=$

$$

$($b$)$ Find the total cost of producing $180$ units.

$($round to $2$ decimal places.$)$

$($c$)$ Find the marginal cost when $180$ units are produced.

$($round to $2$ decimal places.$)$