Solving a Derivative Problem Using the Power Rule

[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?

 

[Hootenanny]

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

Not quite;

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

 

[swears]

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

 

[swears]

Not quite;

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

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

 

[Hootenanny]

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

It comes from the T, remember;

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

 

[swears]

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

 

[dav2008]

See below message.

It comes from the T, remember;

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

 

[Hootenanny]

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

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?

 

[swears]

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

 

[Hootenanny]

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

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

 

[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: $$.5T^{-.5} + .75T^{-.25} + 4T^{-5}$$

 

[dav2008]

I think you need to master algebra before trying calculus.

See: http://www.allaboutcircuits.com/vol_5/chpt_4/5.html

 

[swears]

Thanks, I got it.