Question

What is the derivative of `x + 1/x`?

Answer 1

`1-1/x^2`

Explanation:

We will want to use the power rule, which states that the derivative of `x^n` is `nx^(n-1)`. We can make this rule apply by rewriting the given function:

`f(x)=x+1/x=x^1+x^-1`

Applying the power rule to both, we obtain the derivative:

`f'(x)=1x^(1-1)+(-1)x^(-1-1)`

`f'(x)=1x^0-x^-2`

`f'(x)=1-1/x^2`