Q.A firm's output is given by the production function $Q(L,K) = 4L^2 + 3LK + 2K^2$, where $L$ is labour and $K$ is capital. Find the marginal product of labour and the marginal product of capital when $L=5$ and $K=10$.

Marginal product of labour is $\partial Q/\partial L$ and marginal product of capital is $\partial Q/\partial K$; find both, then substitute $L=5, K=10$. …

Step 1 — Find the marginal product of labour. Differentiate $Q=4L^2+3LK+2K^2$ with respect to $L$, treating $K$ as constant: $MP_L = \dfrac{\partial Q}{\partial L} = 8L+3K$.

Step 2 — Find the marginal product of capital. Differentiate the same $Q$ with respect to $K$, treating $L$ as constant: $MP_K = \dfrac{\partial Q}{\partial K} = 3L+4K$.

Step 3 — Evaluate both at $L=5, K=10$.

$MP_K(5,10) = 3(5)+4(10) = 15+40=55$ …

Differentiating the $3LK$ term incorrectly — e.g. treating it as $3L^2$ or $3K^2$ instead of a genuine cross term — is a common slip; remember $\partial(3LK)/\partial L = 3K$ (the …