The derivative of a function gives us the slope of the tangent line at any point on the curve.
The derivative of $x$ is $1$ and the derivative of $\frac{1}{x}$ is $-\frac{1}{x^2}$. So, the derivative of the function $y=x+\frac{1}{x}$ is $1-\frac{1}{x^2}$.
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