InterviewSolution
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InterviewSolution
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Differentiate `tan^(-1){(x^(1//3)+a^(1//3))/(1-(a x)^(1//3))}`with respect to `x` |
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Answer» Let `y=((x^(1//3)+a^(1//3))/(1-x^(1//3)a^(1//3))).` Putting `x^(1//3)=tan theta and a^(1//3)=tan phi,` we get `y=tan^(-1)((tan theta+tan phi)/(1-tan theta tan phi))=tan^(-1)[tan(theta+phi)]` `=(theta+phi)=tan^(-1)(a^(1//3)).` `therefore(dy)/(dx)=(d)/(dx){tan^(-1)(x^(1//3))+tan^(-1)(a^(1//3))}` `=(d)/(dx){tan^(-1)(x^(1//3))+tan^(-1)(a^(1//3))}.` `=(d)/(dx){tan^(-1)(x^(1//3))}+(d)/(dx){tan^(-1)(a^(1//3))}=(1)/((1+x^(2//3))).(1)/(3)x^(-2//3)` `=(1)/(3x^(2//3)(1+x^(2//3)))" "[because" "tan^(-1)(a^(1//3))="constant"].` |
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