InterviewSolution
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InterviewSolution
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If `y=sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5)))`, find `(dy)/(dx)`. |
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Answer» Given : `y=sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5))).` Taking logarithm on both sides of (i), we get `logy=(1)/(2){log(x-3)+log(x-3)+log(x^(2)+4)-log(3x^(2)+4x+5)}.` Differentiating both sides w.r.t. x, we get `(1)/(y).(dy)/(dx)=(1)/(2).{(1)/((x-3))+(2x)/((x^(2)+4))-((6x+4))/((3x^(2)+4x+5))}` `rArr (dy)/(dx)=((1)/(2)y).{(1)/((x-3))+(2x)/((x^(2)+4))-((6x+4))/((3x^(2)+4x+5))}` `=(1)/(2).sqrt(((x-3)(x^(2)+4))/((3x^(3)+4x+4))).{(1)/((x-3))+(2x)/((x^(2)+4))-((6x+4))/((3x^(2)+4x+5))}` |
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