I need to find the derivative for f(x) = e^x/((e^x+3)(x+3)) and have no idea how to proceed. Everything I have tried has not come out right. How would I approach this problem?

Question

amistre64 · Answer

f(x) = e^x
   ----------  ; its justsa  matter of keeping track of the derivative
  (e^x+3)(x+3)    rules right?

amistre64 · Answer

go ahead and exapnd the bottom to make life easier

anonymous · Answer

$$f'(x)={e^x(e^x+3)(x+3)-e^x[(e^x+3)+e^x(x+3)] \over (e^x+3)^2(x+3)^2}$$. You need to work in the simpilification a little bit.

anonymous · Answer

on*

anonymous · Answer

Anwar, can you show me the steps between so I can understand how you got to that answer? It's correct, but I have no idea how you got to it.

anonymous · Answer

Well, actually there is no steps in between. It's just one step using both quotient and product rules. Let's say that the top is $g(x)$ and the bottom is $h(x)$, then we have this formula:
$$f'(x)=({g(x) \over h(x)})'={h(x)g'(x)-g(x)h'(x) \over (h(x))^2}$$
It's better to find $h'(x)$ first using the product rule and then substitute in $f'(x)$, that would make it easier and would help you to avoid making any mistakes.

anonymous · Answer

Thank you. I understand it now. Looks like I was on the right track but just didn't go far enough.

anonymous · Answer

Good :)