Determine the derivative of the function $$ g(x)=\ln \left(\sqrt[4]{\frac{x+10}{x-10}}\right) $$

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Find the first order derivative with respect to $$ x $$ for $$ \ln\left(\sqrt[4]{\frac{x+10}{x-10}}ight) $$.
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
  $$\frac{d}{dx}\left(\ln{\left(\sqrt[4]{\frac{x+10}{x-10}}ight)}ight)$$
- step1: Use the properties of radicals:
  $$\frac{d}{dx}\left(\ln{\left(\frac{\sqrt[4]{x+10}}{\sqrt[4]{x-10}}ight)}ight)$$
- step2: Use differentiation rules:
  $$\frac{d}{dg}\left(\ln{\left(gight)}ight)	imes \frac{d}{dx}\left(\frac{\sqrt[4]{x+10}}{\sqrt[4]{x-10}}ight)$$
- step3: Find the derivative:
  $$\frac{1}{g}	imes \frac{d}{dx}\left(\frac{\sqrt[4]{x+10}}{\sqrt[4]{x-10}}ight)$$
- step4: Calculate:
  $$\frac{1}{g}	imes \left(-\frac{5}{\sqrt[4]{\left(x+10ight)^{3}\left(x-10ight)^{5}}}ight)$$
- step5: Substitute back:
  $$\frac{1}{\frac{\sqrt[4]{x+10}}{\sqrt[4]{x-10}}}	imes \left(-\frac{5}{\sqrt[4]{\left(x+10ight)^{3}\left(x-10ight)^{5}}}ight)$$
- step6: Calculate:
  $$\frac{\sqrt[4]{x-10}}{\sqrt[4]{x+10}}	imes \left(-\frac{5}{\sqrt[4]{\left(x+10ight)^{3}\left(x-10ight)^{5}}}ight)$$
- step7: Multiply the terms:
  $$-\frac{\sqrt[4]{x-10}}{\sqrt[4]{x+10}}	imes \frac{5}{\sqrt[4]{\left(x+10ight)^{3}\left(x-10ight)^{5}}}$$
- step8: Rewrite the expression:
  $$-\frac{\sqrt[4]{x-10}}{\sqrt[4]{x+10}}	imes \frac{5}{\sqrt[4]{x-10}	imes \left(x\sqrt[4]{\left(x+10ight)^{3}}-10\sqrt[4]{\left(x+10ight)^{3}}ight)}$$
- step9: Reduce the fraction:
  $$-\frac{1}{\sqrt[4]{x+10}}	imes \frac{5}{x\sqrt[4]{\left(x+10ight)^{3}}-10\sqrt[4]{\left(x+10ight)^{3}}}$$
- step10: Multiply the terms:
  $$-\frac{5}{\sqrt[4]{x+10}	imes \left(x\sqrt[4]{\left(x+10ight)^{3}}-10\sqrt[4]{\left(x+10ight)^{3}}ight)}$$
- step11: Multiply the terms:
  $$-\frac{5}{x^{2}-100}$$
The derivative of the function $$ g(x)=\ln \left(\sqrt[4]{\frac{x+10}{x-10}}ight) $$ with respect to $$ x $$ is $$ -\frac{5}{x^{2}-100} $$.
The derivative of $$ g(x) $$ is $$ -\frac{5}{x^{2}-100} $$.

Determine the derivative of the function

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