heres the problem : d/dx (4x^4 -2x)/4x^4 + 2x)
and heres my work, let me know if you see something wrong. a * means multiply.
= 4x^4-2x * (4x^4+2x)^-1
= 16x^3-2 * (4x^4+2x)^-1 + 16x^3+2 * -(4x^4+2x)^-2 * 4x^4-2x
=(16x^3-2) / (4x^4+2x) + (16x^3+2) / (-4x^4-2x)
= factored out a 2 from the tops and a 2x from the bottom
=8x^3-1 / 2x^4+x + 8x^3+1 / 2x^4-x.
= added the 2 terms together (by painfully multiplying the bottoms together ect.)
= 2x^5+2x^4+x^2 / -4x^8-4x^10-x^2
= factor out a x^2
= 2x^3+2x^2+1 / -4x^6-4x^8 - 1.
However im like 99% sure im wrong. What am I doing wrong??
because i just convert it to product rule because that way I dont have to memorize a million rules and i figure its the same thing. Thanks because I see thats the right answer.
Anyway, any idea as to what I did wrong? I spent a long time doing it over and over and it drove me nuts.