Homework Help

Find `y'` for `y=( log_2 x) / (1+x^2)`  

user profile pic

jjmgingrich | Student, Undergraduate | (Level 1) Salutatorian

Posted June 20, 2012 at 3:35 AM via web

dislike 1 like

Find `y'` for `y=( log_2 x) / (1+x^2)`

 

1 Answer | Add Yours

user profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted June 20, 2012 at 3:43 AM (Answer #1)

dislike 1 like

`y=(log_2 x) /(1+x^2)`

==> Use the quotient rule to find the derivative.

==> If y= u/v ==> y'= (u'v-uv')/v^2

==>` y'=((log_2 x)'(1+x^2) - (log_2 x)(1+x^2)')/(1+x^2)^2`

`==> y'= (1/(xln2) (1+x^2) - (log_2 x)(2x))/(1+x^2)^2`

`==> y'= ((1+x^2)/(xln2) - (lnx/ln2)(2x))/(1+x^2)^2`

`==> y'= (1+x^2 - 2x^2 lnx)/(xln2(1+x^2)^2)`

` `

` `

` `

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes