InterviewSolution
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InterviewSolution
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Differentiate `sqrt((x-1)(x-2)(x-3)(x-4))` w.r.t. x. |
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Answer» Let `y=sqrt((x-1)(x-2)(x-3)(x-4))." …(i)"` Taking logarithm on both sides of (i), we get `log y = (1)/(2){log(x-1)+logx(x-2)+log(x-3)+log(x-4)}……..(ii)` On differentiating both sides of (ii) w.r.t. x we get `(1)/(y).(dy)/(dx)=(1)/(2).{(1)/((x-1))+(1)/((x-2))+(1)/((x-3))+(1)/((x-4))}` `(dy)/(dx)=((y)/(2)).{(1)/((x-1))+(1)/((x-2))+(1)/((x-3))+(1)/((x-4))}` `=(1)/(2).sqrt((x-1)(x-2)(x-3)(x-4)).{(1)/((x-1))+(1)/((x-2))+(1)/((x-3))+(1)/((x-4))}` |
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