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and i need to find the function, which apparantly is 1/p |x|^p but i can't figure out how to show this.

This is for a bigger problem where the function must be convex. and also p>1

I tried, finding the derivative of 1/p |x|^p , but i don't get the gradient function.

At first, I thought about this function: 1/p-1 |x|^p-1 where you can easily get the gradient function by taking the derivative but i was told that this is not a convex function.

any help would be greatly appreciated.