Question

Another derivative question.. this time with the quotient rule.. :D
x-3/x^2+x+1

Answer 1

let

\[u(x) = x - 3... so..... u'(x) = 1 \]

and

\[v(x) = x^2 + x + 1...so.....v'(x) = 2x + 1\]

the quotient rule says

\[f'(x) = \frac{v \times u' - u \times v'}{v^2}\]

just substitute and evalaute

Answer 2

\(\large\sf \color{red}{\frac{low\frac{d}{dx}(high)-high \frac{d}{dx}(low)}{(low)^2}}\) that helped me learn quotient rule

Answer 3

low dee high minus high dee low, over low-low. which means: lower function multiplied by derivative of the higher function, MINUS higher function times derivative of the lower function, ALL OVER the lower function twice.

Answer 4

Hm, soo
(x^2 + x + 1)(x-3)' - (x-3)(x^2+x+1)' / (x^2 + x + 1)^2

Answer 5

(x^2 + x + 1)(1) - (x-3)(2x+1)/(x^2+x+1)^2

Answer 6

Write it in LaTex form!!! I can barely understand that! But pretty much yes. I think that looks right

Answer 7

It says to not simplify so that's the final answer.

Answer 8

well actually
(x^2 + x + 1) - (x-3)(2x+1)/(x^2+x+1)^2

Answer 9

No. That's not the answer. Do not simplify means do not try to cancel out any terms. But you STILL need to find the derivative and perform the algebra on the numerator portion such as distribute and such.

Answer 10

Because what you're doing above is just tedious algebra, and you SHOULD be very comfortable with algebra if you're doing Calculus now.

Answer 11

(x^2 + x + 1) - (2x^2 -5x -3) /(x^2+x+1)^2

Answer 12

WHAT DO YOU MEAN LATEX ? I JUST CHECKED THE SOLUTIONS MANUAL
its writtten like this -.-
(x^2 + x + 1)(1) - (x-3)(2x+1)/(x^2+x+1)^2

Answer 13

Use the equation editor button on the bottom!!

Answer 14

\[\frac{ (x^2 + x + 1) - (2x^2 -5x -3) }{ (x^2+x+1)^2 }\]