Gradient of the function $f(x)= \|x\|^p$

Question

How can the gradient in this case be computed? I understand that $f(x)= (x_1^2 + x_2^2 + \ldots + x_N^2)^{p/2}$ but how do I proceed from here?

Answer 1

• Recall the definition of the gradient.

• Recall the definition of partial derivative.

• Recall how to compute the derivative of $(x^2 + C)^{p/2}$.