Question

How do you find the derivative of `(x^2-2)/(x)`?

Answer 1

At first sight we might think of using the quotient rule, but I'd rather operate a division here and simplify things for us. That'll be not only faster but show knowledge on derivation.

We see this function `(x^2-2)/x` can be rewritten as

`x^2/x-2/x`

In turn, it can be rewritten as

`x-2x^-1`

Now, derivating this sounds easier, doesn't it?

`(dy)/(dx)=1-(-2x^-2)`
`(dy)/(dx)=1+2/x^2`