Question

Find de derivative of the function

Answer 1

$y=(x+\frac{1}{x})(x-\frac{1}{x}+1)\\\\\frac{dy}{dx}=(\frac{d}{dx}(x+\frac{1}{x}))((x-\frac{1}{x}+1)+(x+\frac{1}{x})(\frac{d}{dx}(x-\frac{1}{x}+1))\\\\\frac{dy}{dx}=(1-\frac{1}{x^2})(x-\frac{1}{x}+1)+(x+\frac{1}{x})(1+\frac{1}{x^2})\\\\\text{which developing the products gives:}\\\frac{dy}{dx}=2x-\frac{1}{x^2}+\frac{2}{x^3}+1$