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