Suppose that a firm has the production function $${f(x_1,x_2) = x_1^\frac{1}{2} + x_2^2}$$
I know that you have to find the marginal product for both $x_1$ and $x_2$ and those come out to be $x_1 = \frac{1}{2\sqrt x}$ and $x_2 = 2x_2$
Where do I go from here?
*I should add, the answer to this question is that it's neither increasing or decreasing - as verified by my teacher
Your own calculations indicate that the marginal product of $f$ wrt $x_1$ is independent of $x_2$ because the partial of $f$ wrt to $x_1$ doesn't involve $x_2$.