InterviewSolution
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InterviewSolution
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Find `(dy)/(dx)fory=log(x+sqrt(a^2+x^2))dot` |
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Answer» `y=log (x+sqrt(a^(2)+x^(2)))` `"Then "(dy)/(dx)=(d)/(x){log (x+sqrt(a^(2)+x^(2)))}` `=(1)/(x+sqrt(a^(2)+x^(2)))(d)/(dx)(x+sqrt(a^(2)+x^(2)))` `=(1)/(x+sqrt(a^(2)+x^(2)))xx{1+(1)/(2)(a^(2)+x^(2))^(-1//2)(d)/(dx)(a^(2)+x^(2))}` `=(1)/(x+sqrt(a^(2)+x^(2))){1+(1)/(2sqrt(a^(2)+x^(2)))xx2x}` `(1)/(x+sqrt(a^(2)+x^(2)))xx(sqrt(a^(2)+x^(2))+x)/(sqrt(a^(2)+x^(2)))` `=(1)/(sqrt(a^(2)+x^(2)))` |
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