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

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### 1 Answer

`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)`

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