<p>K so I'm self studying BC with Barron's, and right now I'm doing Indeterminates and L'Hopital's Rule. One of the examples they give I'm not sure is right. There's a bunch of stuff in the problem, but it comes down to this:</p>
<p>f(x) = x sin (1/x)
or
f(x) = (sin (1/x)) / (1/x)</p>
<p>What's f'(x)?</p>
<p>Barron's says it's (cos 1/x), but I keep getting:</p>
<p>[-cos (1/x) / x] + sin (1/x)</p>
<p>Is mine just not simplified or what? Btw problem is Example 45 Chapter 3 under J.</p>
<p>I got the same answer. I assume it’s not simplified.</p>
<p>I got Sin(1/x) + Cos(1/x)/x. I personally think that Barron’s book is garbage. I also have that book and whenever I apply what I used in class to answer the problems I always get some completely different answer because the book uses some crazy method.</p>
<p>You’re doing L’Hopital? Are you sure that you’re not being asked to find the derivative of the top and bottom separately?</p>
<p>Doing sin (1/x) / (1/x) separately yields [(-1/x^2)*cos (1/x)] / (-1/x^2) = cos (1/x).</p>
<p>Oh yah, my mistake, thanks yodastreet. I just assumed it was one derivative and x sin (1/x) was the same thing. Barron’s always does like 50 steps in one without any explanation. Got it now anyways, thanks.</p>
<p>No problem, glad it helped.</p>