Stuck on derivative of logarithm of sum of exponentials let's say that I need to calculate the following expression: (delt log(exp(w_1 * x_1 + b_1) + exp(w_2 * x_2 + b_2)))/(del w_1)

Marcelo Mullins

Marcelo Mullins

Answered question

2022-07-18

Stuck on derivative of logarithm of sum of exponentials
let's say that I need to calculate the following expression:
l o g ( e x p ( w 1 x 1 + b 1 ) + e x p ( w 2 x 2 + b 2 ) ) w 1
How do I start? The rules that I know about derivation, exponential and logarithm are not very useful in this situation.

Answer & Explanation

kamphundg4

kamphundg4

Beginner2022-07-19Added 20 answers

This is just an application of the chain rule
l o g ( e x p ( w 1 x 1 + b 1 ) + e x p ( w 2 x 2 + b 2 ) ) w 1 = w 1 ( l o g ( f ( w 1 ) ) = f ( w 1 ) w 1 f ( w 1 )
So your final answer is:
x 1 e x p ( w 1 x 1 + b 1 ) e x p ( w 1 x 1 + b 1 ) + e x p ( w 2 x 2 + b 2 ) )

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