May 10, 2020 · 3 I was studying Multi-variable Calculus, and I got confused with the definition of the Gradient. The definition that I learned was this: But, doing some examples, and searching in Google I …

Oct 1, 2021 · In my case, I'm looking for the gradient of the function with respect to an input in the function, this input being a vector (2d or 3d in that case).

Feb 18, 2015 · The $\nabla \nabla$ here is not a Laplacian (divergence of gradient of one or several scalars) or a Hessian (second derivatives of a scalar), it is the gradient of the divergence. That is why …

Dec 20, 2023 · To my understanding, the gradient essentially packages together all the required partial derivatives of a function in a single structure. In 3 dimensions, the resulting vector gives the slope of st...

Feb 14, 2022 · I've just moved on from single variable to multivariable calculus and having trouble understanding the gradient as I'm trying to draw a comparison b/w single and multivariable …

1 The gradient points to the direction of faster growing of the function. See The Gradient and Directional Derivative.

Aug 11, 2021 · How do you generally define the gradient of a multivariate vector-valued function with respect to two different vectors of different sizes? My attempt has been (using notation from the …

Oct 28, 2012 · 0 Short answer: The "gradient" of a vector-valued function is the Jacobian matrix. More complete answer: I will restrict my use of symbols to those that would be understood by someone …

Apr 11, 2020 · Explore related questions multivariable-calculus partial-derivative vector-analysis See similar questions with these tags.

Jun 18, 2020 · The chain rule tells us that $$ h' (x) = f' (g (x)) g' (x). $$ This formula is wonderful because it looks exactly like the formula from single variable calculus. This is a great example of the …