# Thread: Where am i going wrong on taking the derivative?

1. ## Where am i going wrong on taking the derivative?

The problem is$\displaystyle \frac{t^8+9t+3}{t^2}$

I used the qoutent rule and got$\displaystyle \frac{t^2(8t^7+9)-t^8+9t+3(2t)}{(t^2)^2}$

I ended with $\displaystyle \frac{3t(2t^8+9t+2)}{t^4}$

This work isn't looking like the answer at all. Where am I going wrong?

Thanks

2. Originally Posted by Darkhrse99
The problem is$\displaystyle \frac{t^8+9t=3}{t^2}$

I used the qoutent rule and got$\displaystyle \frac{t^2(8t^7+9)-t^8+9t+3(2t)}{(t^2)^2}$

I ended with $\displaystyle \frac{3t(2t^8+9t+2)}{t^4}$

This work isn't looking like the answer at all. Where am I going wrong?

Thanks
The = in the initial problem is supposed to be a +, I think? Anyway, when you did the Quotient Rule, you forgot to multiply the terms in the numerator (2nd part)....

3. The middle work I left out is $\displaystyle (8t^9+9t^2)-2T^9+18t^2+6t$

doing subtraction gives you$\displaystyle \frac{6t^9+27t^2+6t}{(t^2)^2}$

I did the multiplication in the numerator.

4. Originally Posted by Darkhrse99
The middle work I left out is $\displaystyle (8t^9+9t^2)-2T^9+18t^2+6t$

doing subtraction gives you$\displaystyle \frac{6t^9+27t^2+6t}{(t^2)^2}$

I did the multiplication in the numerator.
I don't follow that... but what I'm saying is, the Quotient Rule gives

$\displaystyle \frac{t^2(8t^7+9)-(t^8+9t+3)(2t)}{t^4},$

which is not what you had.

5. Originally Posted by Darkhrse99
$\displaystyle \frac{t^8+9t+3}{t^2}$
I would break it up into three terms, which seems a lot easier to me.

$\displaystyle \frac{t^8}{t^2}+\frac{9t}{t^2}+\frac{3}{t^2}$

6. Originally Posted by Jameson
I would break it up into three terms, which seems a lot easier to me.

$\displaystyle \frac{t^8}{t^2}+\frac{9t}{t^2}+\frac{3}{t^2}$
Jameson,

Using the qoutent rule, I came up with $\displaystyle \frac{-6t^9+3t^2+6t}{(t^2)^2}$

How can I simplify this more?

7. Originally Posted by AlephZero
I don't follow that... but what I'm saying is, the Quotient Rule gives

$\displaystyle \frac{t^2(8t^7+9)-(t^8+9t+3)(2t)}{t^4},$

which is not what you had.
I had posted this problem the exact way you did in my first post.

8. Originally Posted by Darkhrse99
I had posted this problem the exact way you did in my first post.
When you multiply this out I get $\displaystyle \frac{(8t^9+9t^2)-(2t^9+18t^2+6t)}{t^4}$

Is this correct?

9. Originally Posted by Darkhrse99
The problem is$\displaystyle \frac{t^8+9t+3}{t^2}$

I used the qoutent rule and got$\displaystyle \frac{t^2(8t^7+9)-t^8+9t+3(2t)}{(t^2)^2}$

I ended with $\displaystyle \frac{3t(2t^8+9t+2)}{t^4}$

This work isn't looking like the answer at all. Where am I going wrong?

Thanks
Originally Posted by AlephZero
I don't follow that... but what I'm saying is, the Quotient Rule gives

$\displaystyle \frac{t^2(8t^7+9)-(t^8+9t+3)(2t)}{t^4},$

which is not what you had.
Originally Posted by Darkhrse99
I had posted this problem the exact way you did in my first post.
As you can see, you absolutely did not have it posted that way, and that is the beginning of where your calculations went wrong.

10. Originally Posted by AlephZero
As you can see, you absolutely did not have it posted that way, and that is the beginning of where your calculations went wrong.
You right, I left the bracket's out by mistake and didn't sqaure the $\displaystyle t^2$

Is my math correct though?

11. Originally Posted by Darkhrse99
Jameson,

Using the qoutent rule, I came up with $\displaystyle \frac{-6t^9+3t^2+6t}{(t^2)^2}$

How can I simplify this more?
Originally Posted by Darkhrse99
You right, I left the bracket's out by mistake and didn't sqaure the $\displaystyle t^2$

Is my math correct though?
If your answer is the one above, then I'd have to say no. If you've revised your answer, then you need to provide it, as I haven't seen you give another.

12. Is the answer $\displaystyle 6t^5+\frac{9}{t^2}+\frac{6}{t^3}$?

13. Originally Posted by Darkhrse99
The problem is$\displaystyle \frac{t^8+9t+3}{t^2}$
work smart, not hard.

$\displaystyle \frac{t^8+9t+3}{t^2} = t^6 + 9t^{-1} + 3t^{-2}$

$\displaystyle \frac{d}{dt}\left[t^6 + 9t^{-1} + 3t^{-2}\right] = 6t^5 - 9t^{-2} - 6t^{-3} = 6t^5 - \frac{9}{t^2} - \frac{6}{t^3}$

14. Originally Posted by Darkhrse99
Is the answer $\displaystyle 6t^5+\frac{9}{t^2}+\frac{6}{t^3}$?
No. You have asked where your calculations went wrong, and I have shown you over and again where it is. As I said, you have not done the multiplication in the numerator correctly, because you've neglected to distribute the -1. So, once again, the numerator is

$\displaystyle t^2(8t^7+9)-(t^8+9t+3)(2t)$

$\displaystyle =8t^9+9t^2-2t^9-18t^2-6t$

$\displaystyle =6t^9-9t^2-6t$.

15. Originally Posted by skeeter
work smart, not hard.

$\displaystyle \frac{t^8+9t+3}{t^2} = t^6 + 9t^{-1} + 3t^{-2}$

$\displaystyle \frac{d}{dt}\left[t^6 + 9t^{-1} + 3t^{-2}\right] = 6t^5 - 9t^{-2} - 6t^{-3} = 6t^5 - \frac{9}{t^2} - \frac{6}{t^3}$
I believe you ment $\displaystyle 6t^5-\frac{9}{t^2}-\frac{6}{t^3}$?

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