Using The Power Rule

1. Jun 10, 2006

swears

I tried this derivative problem, but the back of the book shows a different answer then what I got. Can someone explain what I'm doing wrong.

$$3T^5 -5T^.5 + \frac{7}{T}$$

So I did this:

$$15T^4 - 2.5T^-.5 - 7T^-8$$

It's the last part I got wrong I'm not sure why. I converted 7/T to T^-7. Is that right?

2. Jun 10, 2006

Hootenanny

Staff Emeritus
Not quite;

$$\frac{7}{T} = 7T^{-1}$$

3. Jun 10, 2006

swears

hmm, it's not doing the exponents right, u might have too look at the code.

4. Jun 10, 2006

swears

Oh, does the -1 come from the 7 or T?

5. Jun 10, 2006

Hootenanny

Staff Emeritus
It comes from the T, remember;

$$\frac{1}{T} = T^{-1}$$

6. Jun 10, 2006

swears

So $$\frac {1}{2T} = 1T^{-2}$$?

7. Jun 10, 2006

dav2008

See below message.

8. Jun 10, 2006

Hootenanny

Staff Emeritus
Nope, not quite.

$$\frac{1}{2T} = (2T)^{-1}$$

The power applies to all terms of the denominator. However;

$$\frac{1}{T^2} = T^{-2}$$

Does that make sense?

9. Jun 10, 2006

swears

So, you basically just combine the top and bottom terms and negate the exponent.

10. Jun 10, 2006

Hootenanny

Staff Emeritus
The exponent is the most important part. You can't just negate it.

11. Jun 10, 2006

swears

Ok, well I had this other problem Maybe I can get it right here.

$$\frac{t^2 + t^3 -{1}}{t^4}$$

I divided by T^4 and then used the power rule and I got: $$.5T^{-.5} + .75T^{-.25} + 4T^{-5}$$

Last edited: Jun 10, 2006
12. Jun 10, 2006

dav2008

13. Jun 10, 2006

swears

Thanks, I got it.