InterviewSolution
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InterviewSolution
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Find `(dy)/(dx)`, when: `y=(sinx)^(x)+sin^(-1)sqrtx` |
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Answer» Correct Answer - `(sinx)^(x).{x cot x+log sin x}+(1)/(2sqrt(x-x^(2)))` Let `y=u+v,` where `u=(sinx)^(x) and v=sin^(-1)sqrtx` Now, `u=(sinx)^(x) rArr logu=x log sin x` `rArr (1)/(u).(du)/(dx)=x.(cosx)/(sinx)+log sin x.1` `rArr (du)/(dx)=(sinx)^(x).{x cot +log sin x}.` And, `v=sin^(-1)sqrtxrArr(dv)/(dx)=(1)/(sqrt(1-x)).(1)/(2)x^(-1//2)=(1)/(2sqrt(x-x^(2)))` `therefore(dy)/(dx)=(du)/(dx)+(dv)/(dx).` |
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