I know that the Fenchel Conjugate of a function is $$f*(x*) = sup{<x, x*> - f(x)}$$ However, how do I find the Fenchel Conjugate of the function $$f(x) = \frac{1}{p}\sum\limits_{i=1}^n |x_i|^p$$ where 1 < p < $\infty$

I have tried differentiating the equation and taking it to be = 0 but I cannot seem to reach any answer.