So, I am stuck on a problem.
If I need to get the derivative of e^(x)/(x+1), would I use the quotient rule on the ^(x)/(x+1)? I am not certain what to do with the fraction power. Thanks for any help.
$\displaystyle y = e^{\frac{x}{x+1}}$
differentiate, use chain rule,
$\displaystyle y'= e^{\frac{x}{x+1}}. \frac{d}{dx}\left(\frac{x}{x+1}\right)$
Now apply Quotient rule to fraction part.
$\displaystyle y'= e^{\frac{x}{x+1}}\left(\frac{1.(x+1)-x.1}{(x+1)^2}\right)$
$\displaystyle y'= e^{\frac{x}{x+1}}\left(\frac{1}{(x+1)^2}\right)$
$\displaystyle y'= \frac{1}{(x+1)^2}.e^{\frac{x}{x+1}}$