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^{5} L^{78}`.
What is the marginal product of capital?
$$
MP_K = \frac{d q \left( K, L \right)}{dK} = \frac{d K^{5} L^{78}}{dK} = 5 K^{5 - 1} L^{78} = 5 K^{4} L^{78}
$$