Answer
$y'=5(x+\dfrac{1}{x})^{4}(1-\dfrac{1}{x^{2}})$
Work Step by Step
$y=(x+\dfrac{1}{x})^{5}$
Let's rewrite the function like this:
$y=(x+x^{-1})^{5}$
Now, differentiate using the chain rule:
$y'=5(x+x^{-1})^{4}(x+x^{-1})'=5(x+\dfrac{1}{x})^{4}(1-x^{-2})$
$y'=5(x+\dfrac{1}{x})^{4}(1-\dfrac{1}{x^{2}})$
