Final answer:
The second-order partial derivative of the function h(x, y) = 7xe^y + 2y with respect to x is 0 since the first derivative with respect to x is a constant.
Step-by-step explanation:
The question asks for second-order partial derivatives of the function h(x, y) = 7xey + 2y. To find the second-order partial derivative with respect to x, which is δ²h/δx², we need to differentiate the function twice with respect to x.
The first derivative of h with respect to x is 7ey, as ey and 2y are treated as constants during differentiation with respect to x. The second derivative, which is the partial derivative we are seeking, would be 0, since the derivative of a constant is zero.