Using the Quotient Rule to Derive the Equation

[Guest]

Hello. I need help deriving this equation using the quotient rule. I'm having difficulty reaching the correct answer because I've no idea what I'm doing wrong.

Quotient Rule: (u'v - v'u) / (v²)

Equation to derive: (2x-3) / (x²)

What I did:

u= 2x-3       v= x²

u'= 2           v'= 2x

*sustituted into equation to get:

-( 2x² - 6x) / x⁴

The answer should be - (2x - 6) / x³ What am I doing wrong?

 

[deftdog18]

u= 2x-3 ,    u' =2

v= x^2 ,    v'=2x

Using quotient rule,

= (x^2(2) - 2x(2x-3))/x^4

= (2x^2- 4x^2 +6x )/x^4

= -2x^2+6x/ x^4

Which can be simplified as -(2x^2 -6x)/x^4

Seems like you got the correct answer here.. maybe the answer is wrong? 

I checked with cymath as well (http://www.cymath.com/answer.php?q=differentiate%20%20(2x-3)%20%2F%20(x2)), same answer. 

[King112]

You've got the right answer. you can divide the equation by x and you'll get 2x-6 divided by x³. Just divide through by x.

Cheers,

King112