Question

What is the derivative of `(x^2-2)/(x)`?

Answer 1

`frac{d}{dx}(frac{x^2-2}{x}) = 1 + 2/x^2`

Explanation:

`frac{d}{dx}(frac{x^2-2}{x}) = frac{d}{dx}(x-2/x)`

`= 1 + 2/x^2`

Answer 2

`D = (x^2 -2) /x^2`

Explanation:

We know the quotient rule:

It states if we have two functions `u and v` then their derivative is given by

`D u/v = (v (d/(du)) u - u (d/(dv)) v)/ v^2`

Here `u and v` are `(x^2 -2) and x` respectively.

Then,

`D (x^2-2)/x = [x d/dx (x^2-2) - (x^2-2) d/dx x] / x^2`

`= (x * 2x - (x^2-2) * 1)/x^2`

The constant is directly removed.

`= [2x^2 - (x^2 - 2)]/ x^2`

`D = (x^2 -2) /x^2`

This will be the answer of the following problem.