InterviewSolution
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InterviewSolution
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If `y=(sqrtx(x+4)^(3//2))/((4x-3)^(4//3)),` find `(dy)/(dx).` |
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Answer» Given: `y=(sqrtx(x+4)^(3//2))/((4x-3)^(4//3))." ...(i)"` Taking logarithm on both sides of (i), we get `log y = (1)/(2)log x+(3)/(2)log (x+4)-(4)/(3)log(4x-4).` On differentiating both sides w.r.t. x, we get `(1)/(y).(dy)/(dx)=(1)/(2).(1)/(x)+(3)/(2).(1)/((x+4))-(4)/(3).(4)/((4x-3))` `rArr(dy)/(dx)=y[(1)/(2x)+(3)/(2(x+4))-(16)/(3(4x-3))]` `=(sqrtx(x+4)^(3//2))/((4x-3)^(4//3)).[(1)/(2x)+(3)/(2(x+4))-(16)/(3(4x-3))].` |
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