Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How would I solve for this derivative?

$$s=\frac{1}{N} \sum_i^N \left[t_i - \left(\sum_j \left[c_j e^{-\frac{(r_i-r_j)^2}{2w^2}} + b\right]\right)\right]^2$$

I want to solve for $\dfrac{ds}{dw_j}$.

I don't have the first clue on how to solve this. It has been a while since I have done calculus.

share|improve this question

1 Answer 1

up vote 0 down vote accepted

It's not as complicated as it looks, assuming you meant $w_j$ instead of $w$: $$\frac{ds}{dw_j} =\frac{2}{N} \sum_i^N \left[t_i - \left(\sum_j \left[c_j e^{-\frac{(r_i-r_j)^2}{2w_j^2}} + b\right]\right)\right] \cdot \left[ -\frac{(r_i-r_j)^2}{2w_j^2}\cdot \frac{2(r_i-r_j)^2}{2w_j^3}c_j e^{-\frac{(r_i-r_j)^2}{2w_j^2}} \right]$$

share|improve this answer
    
Ah I see now. How could I forget about the chain rule... It really has been to long. Thanks for your help. –  still learning Jun 25 '13 at 19:28

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.