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

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Answer 1 · 2016-01-28T13:19:08

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

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

$= 1 + 2/x^2$

Answer 2 · 2016-01-28T13:31:31

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

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.

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