InterviewSolution
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InterviewSolution
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`y=sqrt(x^2+1) - log(1/x+sqrt(1+1/(x^2)))`, find `dy/dx` |
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Answer» We have `y=sqrt(x^(2)+1)-log{(1+sqrt(x^(2)+1))/(x)}` `rArr y=sqrt(x^(2)+1)-log{1+sqrt(x^(2)+1)}+logx` `rArr(dy)/(dx)=(1)/(2)(x^(2)+1)^(-1//2).2x-(1)/({1+sqrt(x^(2)+1)}).{(1)/(2)(x^(2)+1)^(-1//2).2x}+(1)/(x)` `=(x)/(sqrt(x^(2)+1))-(1)/({1+sqrt(x^(2)+1)}).(x)/(sqrt(x^(2)+1))+(1)/(x)` `=(x{1+sqrt(x^(2)+1}}-x)/((sqrt(x^(2)+1)){1+sqrt(x^(2)+1)})+(1)/(x)=(xsqrt(x^(2)+1))/((sqrt(x^(2)+1)){1+sqrt(x^(2)+1)})+(1)/(x)` `=(x)/({1+sqrt(x^(2)+1)})+(1)/(x)=((x^(2)+1)+sqrt(x^(2)+1))/(x{1+sqrt(x^(2)+1)})` `((sqrt(x^(2)+1)){(sqrt(x^(2)+1))+1})/(x{1+sqrt(x^(2)+1)})=(sqrt(x^(2)+1))/(x)`. |
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