How to differentiate 2lnx - 2/x?

Question

The books says the answer is 2(x+1)/x^2

I'm not sure how to get this. Could you please show me how (including working). Thanks :)

Answer 1

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

Answer 2

Differentiate lnx you get 1/x

Differentiate (-1)/x you get 1/x²

Differentiate 2lnx - 2/x = 2(lnx - 1/x) = 2[(1/x) + (1/x²)]

= 2[(x/x²) + (1/x²)] = 2[(x + 1)/x²]

there you go (:

good luck