u of x? (Given f[x]= (x^2+3x+1)^5 / (x+3)^5, identify...)

[confused_07]

Here's my problem:

Given f[x]= (x^2+3x+1)^5 / (x+3)^5, identify a function u of x and an integer n does not = 1 such that f[x]= u^n. Then compute f'[x].

I understand that I have to use the Quotient Rule to get the derivative, but I am not grasping how to identify the function u of x. Can someone point me in the right direction?

Thank you

 

[pka]

Just simple division gives:
\(\displaystyle \L\begin{array}{l}
\frac{{\left( {x^2 + 3x + 1} \right)^5 }}{{\left( {x + 3} \right)^5 }} = \left( {x + \frac{1}{{x + 3}}} \right)^5 \\
\frac{d}{{dx}}\left( {x + \frac{1}{{x + 3}}} \right)^5 = 5\left( {x + \frac{1}{{x + 3}}} \right)^4 \left( {1 - \frac{1}{{\left( {x + 3} \right)^2 }}} \right) \\
\end{array}\)

 

[confused_07]

What did they mean by identifying a function u of x? Is that what you just did, or am I supposed to make a new function f[x]=u^n?