Simple Derivation giving me a headache.

1. Jan 18, 2012

Jimbo57

1. The problem statement, all variables and given/known data
Deriving http://www4d.wolframalpha.com/Calculate/MSP/MSP20181a00e6i82g005gag00005gb4c7hic8g2i3hi?MSPStoreType=image/gif&s=57&w=79&h=43 [Broken]

2. Relevant equations

3. The attempt at a solution

My attempt gives me:
-48/(x^2-16)^2 + 192x^2/(x^2-16)^3 via product rule

Wolfram alpha gives me this for an answer

http://www4d.wolframalpha.com/Calculate/MSP/MSP40371a00e53i06h6352d000061574g9ehi6a9958?MSPStoreType=image/gif&s=15&w=224&h=48 [Broken]

I can't seem to figure out how to match my answer with Wolfram, even though it's not a tough derivative. Am I maybe not simplifying enough?

Last edited by a moderator: May 5, 2017
2. Jan 18, 2012

Curious3141

A simple trick that you can use to see if your answer actually matches up is to let x be a transcendental number like $\pi$ in your answer, then in Wolfram's. Since we're dealing with rational coefficients and exponents throughout, there is no way they can match up unless the answers are algebraically equivalent. They do match up in this case.

So it's just a matter of rearranging your equation. Try reexpressing -48/(x^2-16)^2 as $-\frac{48(x^2 - 16)}{{(x^2 - 16)}^3}$ for starters, then combine the numerators over a common denominator.

Last edited by a moderator: May 5, 2017
3. Jan 18, 2012