1. ## Quotient Rule maybe?

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.

$y = e^{\frac{x}{x+1}}$

differentiate, use chain rule,

$y'= e^{\frac{x}{x+1}}. \frac{d}{dx}\left(\frac{x}{x+1}\right)$

Now apply Quotient rule to fraction part.

$y'= e^{\frac{x}{x+1}}\left(\frac{1.(x+1)-x.1}{(x+1)^2}\right)$

$y'= e^{\frac{x}{x+1}}\left(\frac{1}{(x+1)^2}\right)$

$y'= \frac{1}{(x+1)^2}.e^{\frac{x}{x+1}}$