The gradient of the function |x-y| raised to the power of -3 is given by the equation ∇_{x}|x-y|^{-3} = -(x-y)|x-y|^{-3}. This conclusion is derived using a piecewise approach, which is essential for handling the absolute value in vector calculus. The discussion emphasizes the importance of understanding vector operations and the application of gradients in multivariable calculus.
PREREQUISITESStudents in advanced mathematics, particularly those studying vector calculus, as well as educators and tutors looking to clarify concepts related to gradients and absolute value functions.
Yes, the piecewise approach is what you should be using here.Estane said:Homework Statement
Show that ∇_{x}|x-y|-3= -(x-y)|x-y|-3
x and y are vectors.
Homework Equations
The Attempt at a Solution
When dealing with just a straight up absolute value I know that a solution can be found by using a piece wise approach, but I don't think that's what I should be using here. The power is throwing me completely and I have no idea how to deal with it.
Thanks