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Find the derivative of f(x)\, with respect to x\,: f(x)={\frac  {1}{{\sqrt[ {4}]{x}}}}\,

Remember that all roots can be rewritten as fractional powers.

f(x)={\frac  {1}{{\sqrt[ {4}]{x}}}}={\frac  {1}{x^{{{\frac  {1}{4}}}}}}=x^{{-{\frac  {1}{4}}}}\,

Now, taking the derivative is done by the power rule.

f'(x)=-{\frac  {1}{4}}x^{{-{\frac  {5}{4}}}}\,

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