Which of the following is the slope of the production function with respect to an input?

a. For any production function of the form y = f(x1,x2,x3,...,xn) where (x1,x2,x3,...,xn) is an n-dimensional vector of input goods, the slope of the production function with respect to any given input 'i' is a, the marginal physical product of the input. Mathematically speaking, this would be represented by the partial derivative df/dxi, where xi is the ith good.