# Math Help - Second-order total differential

1. ## Second-order total differential

Consider the production function:
y(x1, x2) = x2/1 + x2/2

* i put the "/" signs just to show the first number above the 2nd, its not actually divided*
can someone try to explain how I go about finding the second-order total differential to find if it is concave or convex?
I'd appreciate it if you can explain as simply as possible(in words not math)

2. Do you mean $y(x_1, y_1)= x_1^2+ x_2^2$? If so, a better notation would be y(x_1, x_2)= x_1^2+ x_2^2.
The total differential is $dy= 2x_1 dx_1+ 2x_2 dx_2$ and the "second order" total differential is 0 because there is no term "mixing" the two variables.
If the problem had been $y(x_1, x_2)= x_1^2+ 3x_1x_2+ x_2^2$, then the total differential would have been $dy= (2x_1+ 3x_2)dx_1+ (3x_1+ 2x_2)dx_2$ and the second order differential would have been $3 dx_1dx_2$