Consider the Cobb$-$Douglas production function. Find the marginal productivity of labor $($ L $)$ and the marginal productivity of capital $($K$)$ of the given functions, match the answers to the appropriate functions. Note: Find the MP $($L$)$ and MP$($K$)$ of all the functions first.

$f(L,K)=9L^{0\mathrm{.}4}{K}^{0\mathrm{.}6}f(L,K)=4L^{0\mathrm{.}9}{K}^{0\mathrm{.}1}|f(L,K)||=11K^{0\mathrm{.}3}{L}^{0\mathrm{.}7}f(L,K)=6K^{0\mathrm{.}9}{L}^{0\mathrm{.}1}$

$MP(L)=\frac{3\mathrm{.}6K^{0\mathrm{.}1}}{L^{0\mathrm{.}1}}$

$MP(L)=\frac{0\mathrm{.}6K^{0\mathrm{.}9}}{L^{0\mathrm{.}9}}$

$MP(K)=\frac{5\mathrm{.}4L^{0\mathrm{.}4}}{K^{0\mathrm{.}4}}$

$MP(K)=\frac{3\mathrm{.}3L^{0\mathrm{.}7}}{K^{0\mathrm{.}7}}$