Help with a derivation question.

I don't particularly like using the quotient rule, but here goes

[ (5x^4-20x^3 +1)(x^3) - ( x^5-5x^4+x )(3x^2)] /  x^6

[ 5x^7 - 20x^6 + x^3  - 3x^7 + 15x^6 - 3x^3]  / x^6  

[2x^7 - 5x^6 -2x^3] / x^6  =

[2x^7]/ x^6   -  [5x^6]/x^6   -  [2x^3]/ x^6  

2x   -  5     -  2 / x^3

And there you are.....!!!!

Hi CPhill! 

Thank you so much for answering my question. However, I just have one question. Why do you divide by x^6? 

Remember....in the quotient rule, the denominator is the "v" term squared.......so

v = x^3

And

v^2   = [x^3]^2   = x^6