In my AI textbook there is this paragraph, without any explanation. The sigmoid function is defined as follows $$\\sigma (x) = \\frac{1}{1+e^{-x}}.$$ This function is easy to differentiate

In sum, the gradient is a vector with the slope of the function along each of the coordinate axes whereas the directional derivative is the slope in an arbitrary specified direction.

As you can see, the gradient is perfectly well defined without coordinates. What Alice and Bob will not agree on, is the coordinate expression of their gradients.

Sep 17, 2013 · @HermanJaramillo, Gradient is a vector, and the second formula IS a vector, since $\nabla a$ is a dyadic.

We just learned what the gradient of a function is. It means the largest change in a function. It is the directional derivative. However I have also seen notation that lists the gradient squared ...

Mar 17, 2021 · Could anyone explain in simple words (and maybe with an example) what the difference between the gradient and the Jacobian is? The gradient is a vector with the partial …

Oct 7, 2015 · The gradient is vector valued - each partial derivative corresponds to a component of the gradient vector.

Sep 5, 2019 · The function is two-dimensional, as in, it takes in two real numbers as input. The domain of the function is the plane, so the gradient also lives in the plane. Yes, the graph is …

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Mar 24, 2017 · I'm not sure on how to find the gradient in polar coordinates. The thing that troubles me the most is how to find the unit vectors $\hat {r}$ and $\hat {\theta}$.