How do you derive this?

Question

(x^2 + 1)/x

Answer 1

(x^2 + 1) / x = (x^2/x) + (1/x) = x + 1/x = x + x^-1

Assuming derivative is wrt. itself i.e., dx, you derive as follows:

d(x) / dx = 1

d(x^-1) / dx = -x^-2

So the answer can be written in many different ways as:

    1 - 1/x^2    or     1 - (1/x)^2     or    1 - x^-2

cheers...

Answer 2

-x(x^2+1)^(-x^0)+2x