Can you solve the Kronecker identity?

[spaghetti3451]

I'd like to see how many people can explain this identity:

$$\frac{\partialx_{i}}{\partialx_{j}} = \delta_{ij}$$

 

[spaghetti3451]

$$\frac{\partial x_{i}}{\partial x_{j}} = \delta_{ij}$$

 

[spaghetti3451]

is what i meant.

 

[TylerH]

It means that ∂x_i / ∂x_j is 1 if i=j and 0 if i≠j. In general δ_i,j is 1 if i=j and 0 if i≠j.

 

[Char. Limit]

If i=j, then the partial derivative of x_i with respect to itself is 1. If i does not equal j, then assuming that x_i is not dependent on x_j, then the partial derivative of x_i with respect to x_j is 0. The Kronecker Delta is defined such that the same holds true (when i=j, it's equal to 1, and otherwise it's 0).