# 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.