Guys I'm trying to solve this problem but I'm having difficulties, here is what I tried:
[math]\lim_{{x}\to 0} \frac{\sqrt[n]{c+x} - \sqrt[n]{c-x}}{x}, c>0, n\in \mathbb{N}[/math]
[math]\lim_{{x}\to 0} \frac{\sqrt[n]{c+x} - \sqrt[n]{c-x}}{x} \times \frac{\sqrt[n]{c+x}^{n-1}+ \cdots + \sqrt[n]{c-x}^{n-1}}{\sqrt[n]{c+x}^{n-1}+ \cdots + \sqrt[n]{c-x}^{n-1}} = \lim_{{x}\to0}\frac{2}{\sqrt[n]{c+x}^{n-1}+ \cdots + \sqrt[n]{c-x}^{n-1}}[/math]
how should I continue or should I use another approach?
[math]\lim_{{x}\to 0} \frac{\sqrt[n]{c+x} - \sqrt[n]{c-x}}{x}, c>0, n\in \mathbb{N}[/math]
[math]\lim_{{x}\to 0} \frac{\sqrt[n]{c+x} - \sqrt[n]{c-x}}{x} \times \frac{\sqrt[n]{c+x}^{n-1}+ \cdots + \sqrt[n]{c-x}^{n-1}}{\sqrt[n]{c+x}^{n-1}+ \cdots + \sqrt[n]{c-x}^{n-1}} = \lim_{{x}\to0}\frac{2}{\sqrt[n]{c+x}^{n-1}+ \cdots + \sqrt[n]{c-x}^{n-1}}[/math]
how should I continue or should I use another approach?