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