Example
In the cookie factory, the production function is
$$ q \left( K, L \right) = K L^2 $$The marginal product of capital is
$$ MP_K = \frac{d q \left( K, L \right)}{d K} = L^2 $$Question
In the cookie factory, the production function is `q \left( K, L \right) = K^{30} L^{62}`.
What is the marginal product of capital?
$$
MP_K = \frac{d q \left( K, L \right)}{dK} = \frac{d K^{30} L^{62}}{dK} = 30 K^{30 - 1} L^{62} = 30 K^{29} L^{62}
$$