Originally Posted by
demi can someone please help me with this problem....
.e^(x/2)
----------
..x^(5)
can someone please give me an idea of how to do this problem... thank you!!
Lets assume that you are asking about the derivative of:
$\displaystyle \frac{e^{x/2}}{x^5}$.
Well this can be done in a number of ways, you could use the quotient rule,
or the product rule to find this derivative. Now I don't have that good a
memory, and so never bother with the quotient rule, always using the product rule:
$\displaystyle \frac{d}{dx} f(x)g(x)=\frac{df}{dx}g(x)+f(x)\frac{dg}{dx}$.
Here we let:
$\displaystyle f(x)=e^{x/2}$,
and:
$\displaystyle g(x)=\frac{1}{x^5}$.
Now:
$\displaystyle \frac{d}{dx}f=\frac{d}{dx}e^{x/2}=\frac{1}{2}e^{x/2}$,
and:
$\displaystyle \frac{d}{dx}g=\frac{d}{dx}\left\{ \frac{1}{x^5} \right\}=-5\frac{1}{x^6}$.
So now you have enough to assemble the derivative
RonL