In Linear regression the gradient of the loss with respect to w, have same shape as w so does it mean that the differentiation will take the dimension of the variable with which I'm differentiating?

Course Q&A Deep Learning Specialization Convolutional Neural Networks
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#week2
#LinearRegressionImplementation

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You filed this under DLS C4, which is about Convolutional Networks and Linear Regression is not a topic in DLS C4. I’m guessing maybe you are talking about one of the MLS courses.

It’s also a good idea to put the long sentences in the body of the post and keep the title something relatively short, but expressive.

Yes, you’re right that the gradients are of J (the cost) with respect to one of the parameter variables we need to learn, such as w or b. So it is a partial derivative of J, but it will have the shape of the variable that it is “with respect to”, meaning w and b. That makes sense because the purpose of the gradient is to update w or b, right? So it needs to be the same shape and type as the “target” variable.