(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For complex numbers [itex]f[/itex] and [itex]g[/itex], and for [itex]1<p<\infty[/itex] we have [itex]\lim_{t\rightarrow 0}\dfrac{|f+tg|^p-|f|^p}{t}=|f|^{p-2}(\bar{f}g+f\bar{g})[/itex]; i.e., [itex]|f+tg|^p[/itex] is differentiable.

I would like to show that the above statement is true.

2. Relevant equations

3. The attempt at a solution

I have try several attempts in the direction of manipulating the convex function [itex]|x|^p[/itex]. But no reasonable conclusions yet.

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# Homework Help: Limit and diffirentiability of a function

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