<p>So my Calc class is about to tes over curve sketching, and I know how to graph rational and polynomial functions. My instructor said she'd gives us the derivates of the rational functions to help speed us up sinc eit cna get so messy. For the hw assignment she's letting us turn in in place of a quiz grade however, I have a rational function that reads: x^2/(1+x^4). I don't want help solving the problem, I'm just curious if there's an easier way to fin dthe second derivative than the way Im doing it or if there's a site that will find derivatives for you. I got that the first derivative is 2x(1-x^4)/(1+x^4)2. But when I start looking for the second derivate I'm getting astronomical exponents, and a ton of numbers. What we're being tested over is finidng critical numbers, possible poiunts of inflection, vertical asymptotes, horizontal asymptotes (by testing limits at infinity), symmetry, etc. I don't consider it dishonest to want to know the 2nd derivative, because this is just an assignment she threw together since we complained we needed a drop grade, and since she always gives us the derivates of rational functions on the quizzes (not polynomial or rational exponent, just rational function). If anyone could give me a tip or a site with a deriv tool, I'd appreciate it.</p>
<p>Just use a TI-89, or the quotient rule. Be lucky you don't have to integrate that.</p>
<p>2x(1-x^4)/(1+x^4)2
(2x-2x^5)/(1+x^4)2
..
Quotient Rule,
(low<em>d(high) - high</em>d(low)) / low^2</p>
<h2>(1+x^4)^2<em>(2-10x^4))-(2x-2x^5)</em>(2(1+x^4)*x^3)</h2>
<pre><code> (1+x^4)^4
</code></pre>
<p>Simply(preferably), then Quotient rule again.</p>
<p>I'll never forget that stupid rhyme...</p>
<p>low dhigh minus high dlow, all over whats below.............squared.</p>
<p>I learned "HO dHI - HI dHO, over the square of HO we go"</p>
<p>dbottom dtop minus dtop d bottom over bottom squared.</p>
<p>You could always use ln differentiation.</p>
<p>I always try find ways to avoid using the quotient rule.</p>
<p>One could also convert the function as a product of two polynomials, (x^2)(x^4+1)^-1 and use the product rule, which I find easier than the quotient rule.</p>
<p>It is.... but the AP exam will expect you to solve it out via Quotient rule. If you do it otherwise, your answer... although yes would be the same, the form would be different, and therefore useless for the multiple choice section.</p>
<p>So then the second derivative is: (10x^4 - 14x^12 - 22x^8 -2) / (1+ x^4)^4</p>
<p>Shoot me. All that work only to find out there are no possible points of inflection :(</p>