InterviewSolution
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InterviewSolution
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Differentiate w.r.t `x: sin^(-1) ((2^(x+1))/(1+4^x))` |
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Answer» Correct Answer - `(2^(x+1)(log2))/((1+4^(x)))` Let `y=sin^(-1){(2^(x).2)/(1+(2^(x))^(2))}`. Putting `2^(x)=tan theta`, weget `y=sin^(-1){(2tan theta)/(1+tan^(2)theta)}=sin^(-1)(sin 2theta)=2theta=2tan^(-1)2^(x).` `therefore(dy)/(dx)=2.(d)/(dx)(tan^(-1)2^(x))=2.(1)/({1+(2^(x))^(2)}).(d)/(dx)(2^(x))=(2)/((1+4^(x))).2^(x)(log2)=(2^(x+1)(log2))/((1+4^(x)))` |
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