# How do you differentiate #xe^(x^2+y^2)#?

##### 1 Answer

To differentiate a two-variable function, you need to build the gradient. The gradient is a vector with as many coordinates as the variables the function depends on.

Each coordinate of the vector is a derivative with respect to one of the variables. So, in the two-variables case, you need to calculate the derivatives with respect to

Since deriving with respect to a variable means to consider the other as a constant, it's easier to derivate your function if it's expressed in the form

So, deriving with respect to

Where the derivative of

The derivative with respect to

The gradient is thus the vector