g(x) = x^2 - \frac{1}{x} \text{ where } x \in \mathbb{R} - Leaving Cert Mathematics - Question 5(a) - 2022

To find the derivative of the function, we will differentiate term by term.

The function is given by:

$g(x) = x^2 - \frac{1}{x}$

1. Differentiate the first term, $x^2$, which gives: $\frac{d}{dx}(x^2) = 2x$

2. Next, differentiate the second term, $-\frac{1}{x}$: $\frac{d}{dx}(-\frac{1}{x}) = \frac{1}{x^2}$

3. Combining these results, we get:

   $g'(x) = 2x + \frac{1}{x^2}$

Therefore, the derivative of g(x) is:

$g'(x) = 2x + \frac{1}{x^2}$