Correct Answer - `x^((x^(2)-3)).{((x^(2)-3))/(x)+(2x)logx}+(x-3)^(x^(2)).{(x^(2))/((x-3))+2xlog(x-3)}`
Let `u=x^((x^(2)-3)) and v=(x-3)^(x^(2)).` Then, `y=u+v`
Now, `u=x^((x^(2)-3))`
`rArr logu=(x^(2)-3) logx`
`rArr (1)/(u).(du)/(dx)=(x^(2)-3).(1)/(x)+(2x)logx`
`rArr(du)/(dx)=u.[(x^(2)-3)/(x)+(2x)logx]=x^((x^(2)-3)).{((x^(2)-3))/(x)+(2x)logx}.`
And, `v=(x-3)^(x^(2))`
`rArr log v=x^(2)log(x-3)`
`rArr (1)/(v).(dv)/(dx)=x^(2).(1)/((x-3))+2x log (x-3)`
`rArr(dv)/(dx)=v.{(x^(2))/((x-3))+2xlog(x-3)}=(x-3)^(x^(2)){(x^(2))/((x-3))+2xlog(x-3)}.`
