# Back propagation equations

**URL:** <https://community.deeplearning.ai/t/back-propagation-equations/473347>\
**Category:** Neural Networks and Deep Learning\
**Tags:** coursera-platform\
**Created:** [October 19, 2023, 4:56pm UTC](https://community.deeplearning.ai/t/back-propagation-equations/473347 "2023-10-19T16:56:39Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![mahdi\_khoshmaramzade](https://avatars.discourse-cdn.com/v4/letter/m/2bfe46/32.png) [@mahdi\_khoshmaramzade](https://community.deeplearning.ai/u/mahdi_khoshmaramzade)\
**Post date:** [October 19, 2023, 4:56pm UTC](https://community.deeplearning.ai/t/back-propagation-equations/473347/1 "2023-10-19T16:56:40Z")

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Hi  
in C1,W3, I proofed myself all of 6 equations for one training example.  
In the picture below, I am OK with all equations in left side. The thing I don’t get it is why in right side we sum Db?  
besides , why we don’t sum dWs?

 ![grad_summary](https://global.discourse-cdn.com/dlai/original/3X/1/8/184054fb6df37a57e0fda1b7022ead543c5e6710.jpeg)

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**Author:** ![hackyon](https://sea1.discourse-cdn.com/dlai/user_avatar/community.deeplearning.ai/hackyon/32/64679_2.png) [@hackyon](https://community.deeplearning.ai/u/hackyon)\
**Post date:** [October 20, 2023, 11:32am UTC](https://community.deeplearning.ai/t/back-propagation-equations/473347/2 "2023-10-20T11:32:03Z")

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In the slide you presented, the right side equations are just the vectorized versions of the left side equations.

I believe you are talking about computing the right side (vectorized) of db[1]? This is just the vectorized version of the same equation for db[1] on the left side. Instead of the derivative for one sample in the left side, we sum up the derivatives for multiple samples on the right side.

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**Author:** ![mahdi\_khoshmaramzade](https://avatars.discourse-cdn.com/v4/letter/m/2bfe46/32.png) [@mahdi\_khoshmaramzade](https://community.deeplearning.ai/u/mahdi_khoshmaramzade)\
**Post date:** [October 22, 2023, 8:04am UTC](https://community.deeplearning.ai/t/back-propagation-equations/473347/3 "2023-10-22T08:04:19Z")

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Thanks for your response.