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