# derivative.. problem

• Jan 23rd 2010, 09:43 AM
wolfhound
derivative.. problem
Hello,
I need help , can someone show me how to find the derivative of the problem in the attached photo
• Jan 23rd 2010, 09:54 AM
drumist
$\displaystyle f(t)=\left(t+\frac{1}{t}\right)^{-2}$

$\displaystyle f'(t) = -2 \left(t+\frac{1}{t}\right)^{-3} \cdot \left(t+\frac{1}{t}\right)'$

Can you finish from here? This is using the chain rule.
• Jan 23rd 2010, 10:05 AM
wolfhound
$\displaystyle \left(t+\frac{1}{t}\right)'$

Can you finish from here? This is using the chain rule.

,I'm not sure what the derivative is of this part is????
could you show me how to complete it please?
Can the quotient rule not be used..
• Jan 23rd 2010, 10:27 AM
VonNemo19
Quote:

Originally Posted by wolfhound
$\displaystyle \left(t+\frac{1}{t}\right)'$

Can you finish from here? This is using the chain rule.

,I'm not sure what the derivative is of this part is????
could you show me how to complete it please?
Can the quotient rule not be used..

$\displaystyle \frac{d}{dt}\left[t+\frac{1}{t}\right]=\frac{d}{dt}[t+t^{-1}]=1-t^{-2}=1-\frac{1}{t^2}$
• Jan 23rd 2010, 10:43 AM
wolfhound
Thanks for the help!
But, is this the final answer?
• Jan 23rd 2010, 10:46 AM
VonNemo19
Quote:

Originally Posted by wolfhound
Thanks for the help!
But, is this the final answer?

No. It is only the part that you asked for. The final answer would be:

$\displaystyle f'(t)=-2\left(t+\frac{1}{t}\right)^{-3}\left(1-\frac{1}{t^2}\right)$
• Jan 23rd 2010, 10:52 AM
wolfhound
Quote:

Originally Posted by VonNemo19
No. It is only the part that you asked for. The final answer would be:

$\displaystyle f'(t)=-2\left(t+\frac{1}{t}\right)^{-3}\left(1-\frac{1}{t^2}\right)$

Thanks ,I meant was my bit in the photo the final answer,I was wrong as usual ..
so it cannot be multiplied or simplified any further?
• Jan 23rd 2010, 11:01 AM
VonNemo19
Quote:

Originally Posted by wolfhound
Thanks ,I meant was my bit in the photo the final answer,I was wrong as usual ..
so it cannot be multiplied or simplified any further?

Imean, sure but I know that I wouldn't mess with it anymore unless I was trying to do something with it. Maybe I would write

$\displaystyle f'(t)=-2\frac{\frac{t^2-1}{t^2}}{\frac{(t^2+1)^3}{t^3}}$ and simplify.
• Jan 23rd 2010, 11:27 AM
wolfhound
Oki doki man,
Thanks for your help