Calc2.8

From Exampleproblems

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.

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