anonymous 4 years ago derivative of (t-1/t)

1. anonymous

For t!=0, f(t) = 1-(1/t). Do you know how to derive that?

2. anonymous

Do you mean $\frac{t-1}{t}$ or $t-\frac{1}{t}$?

3. anonymous

the second one

4. anonymous

Oh nvm forget my answer then.

5. anonymous

Well you're just doing two separate derivatives then. One for t, and one for -1/t. Can you do these separately?

6. anonymous

no i wouldn't have asked othewrwise

7. anonymous

i think the derivative of t is zero

8. anonymous

You don't know what the derivative of t is?

9. anonymous

or 1

10. anonymous

No, 0 is only the derivative of a constant. For example, the derivative of the number 5 is 0. t is a variable that changes, so its derivative can't be 0 (that would imply it's not changing). Yes, 1 is correct for t.

11. anonymous

now -1/t?

12. anonymous

Use to power rule: $\frac{d}{dx}x^n = n\cdot x^{n-1}$ In the first case, n = 1, and in the second case n = -1.

13. anonymous

If you know the power rule, you can use it to derive -1/t by first rewriting it as $-t^{-1}$

14. anonymous

thank wio