Suppose that the production function is

f$($x$1,$ x$2)=($x$1)$

$1$

$3($x$2)$

$1$

$3.$

$($a$)$ Write the expression for the marginal product of input x$1.$

$($b$)$ What is the marginal rate of technical substitution between x$2$ and x$1?$

$($c$)$ Does this production function have diminishing rate of technical substitution?

$($d$)$ Does the production function exhibit decreasing, constant, or increasing returns to

scale?