Derivative of a simple exp objective function

Question

Consider the following objective function:

$$\arg\min_\delta \frac{1}{n}\sum_{j=1}^d \sum_{i=1}^n (\delta \times \exp(\frac{-x_i\times j}{c}) - y_i)^2$$

$c$ is a constant, and $n$ is the number of $(x_i,y_i)$ pairs which are in $[0,1]$ and given for all $n$ instances. We'd like to find $\delta$ that minimizes the above objective function.

Is this the correct answer?

$\delta = \sum_{j=1}^d \sum_{i=1}^n y_i \times \exp(\frac{x_i\times j}{c})$

Answer 1

well, the answer to this question is:

$$ \delta = \frac{\sum_{i=1}^n y_i} {\sum_{j=1}^d \sum_{i=1}^n \exp(\frac{-x_i\times j}{c})}$$