Answer
$y ' = 3x^{2}- \frac{1}{x^{2}} +10x +2$
Work Step by Step
Using product rule:
$y = (x^{2}+1)(x+5+\frac{1}{x})$
$y'= (x^{2}+1)(1-\frac{1}{x^{2}}) + (x+5+\frac{1}{x})(2x)$
$y ' = 3x^{2}- \frac{1}{x^{2}} +10x +2$
Using sum of simpler terms:
$y = x^{3} +5x^{2} + 2x + \frac{1}{x} +5$
$y' = 3x^{2}+10x+2-\frac{1}{x^{2}}$
$y ' = 3x^{2}- \frac{1}{x^{2}} +10x +2$
