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

Jan 28, 2016

$\frac{d}{\mathrm{dx}} \left(\frac{{x}^{2} - 2}{x}\right) = 1 + \frac{2}{x} ^ 2$

#### Explanation:

$\frac{d}{\mathrm{dx}} \left(\frac{{x}^{2} - 2}{x}\right) = \frac{d}{\mathrm{dx}} \left(x - \frac{2}{x}\right)$

$= 1 + \frac{2}{x} ^ 2$

Jan 28, 2016

$D = \frac{{x}^{2} - 2}{x} ^ 2$

#### Explanation:

We know the quotient rule:

It states if we have two functions $u \mathmr{and} v$ then their derivative is given by

$D \frac{u}{v} = \frac{v \left(\frac{d}{\mathrm{du}}\right) u - u \left(\frac{d}{\mathrm{dv}}\right) v}{v} ^ 2$

Here $u \mathmr{and} v$ are $\left({x}^{2} - 2\right) \mathmr{and} x$ respectively.

Then,

$D \frac{{x}^{2} - 2}{x} = \frac{x \frac{d}{\mathrm{dx}} \left({x}^{2} - 2\right) - \left({x}^{2} - 2\right) \frac{d}{\mathrm{dx}} x}{x} ^ 2$

$= \frac{x \cdot 2 x - \left({x}^{2} - 2\right) \cdot 1}{x} ^ 2$

The constant is directly removed.

$= \frac{2 {x}^{2} - \left({x}^{2} - 2\right)}{x} ^ 2$

$D = \frac{{x}^{2} - 2}{x} ^ 2$

This will be the answer of the following problem.