Question

Can you calculate the first and second derivative of `(x^3+1)/x^2` ?

`(x^3+1)/x^2`

Answer 1

Please see below.

Explanation:

Let `y = (x^3+1)/x^2`

We could use the quotient rule to find `y'` and `y''`, but I prefer to rewrite the expression:

`y = (x^3+1)/x^2 = x^3/x^2+1/x^2 = x+x^-2`

So, `y' = 1-2x^-3`

And `y '' = 6x^-4`

If we want to write the derivatives as single fractions, we can do so.

`y' = (x^3-2)/x^3`

And `y '' = 6/x^4`