Calculus 8th Edition

$y'= 5(x+\frac{1}{x})^4(1-\frac{1}{x^2})$
Derive the expression using the chain rule: $y=(x+\frac{1}{x})^5$ Apply the chain rule: $f(g(x)) = f'(g(x))g'(x)$: Set $g(x)$ equal to $u$ $g(x) = u = x + \frac{1}{x}$ $g'(x) = u' = 1 - \frac{1}{x^2}$ $y(u) = (u)^5 u'$ $y'(u) = 5(u)^4u'$ $y' = 5(x + \frac{1}{x})^4 ( 1 - \frac{1}{x^2})$