Question

Partial Differentiation problem, see attachment below please:

Answer 1

Text version:

Consider:
\[f(x,y)=\sum_{j=1}^{N}c_{j}\phi(r_{j};\epsilon)\]

where c1,....cn are coefficients , N is the number of data points,

\[r_{j}=[(x-x_{j})^2+(y-y_{j})^2]^\frac{1}{2}\]

and

\[\phi(r;\epsilon)=\sqrt{1+(\epsilon \times r)^2} \]

for some parameter epsilon.

Differentiate (1) to find expressions for partial derivatives

Answer 2

I'm not familiar with this function, but in general the derivative of a sum is the sum of the derivatives. From there it'll be a matter of the chain rule.