InterviewSolution
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InterviewSolution
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`"If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y_(2)+xy_(1)` is (where `y_(r)` represents the rth derivative of y w.r.t. x)A. `m^(2)y`B. `my^(2)`C. `m^(2)y^(2)`D. none of these |
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Answer» We have `y^(1//m)=(x+sqrt(1+x^(2)))` `"or "y=(x+sqrt(1+x^(2)))^(m)` `"or "(dy)/(dx)=m(x+sqrt(1+x^(2)))^(m-1)(1+(x)/(sqrt(x^(2)+1)))` `=m((x+sqrt(1+x^(2)))^(m))/(sqrt(1+x^(2)))` `=(my)/(sqrt(1+x^(2)))` `"or "y_(1)^(2)(1+x^(2))=m^(2)y^(2)` `"or "2y_(1)y_(2)(1+x^(2))+2xy_(1)^(2)=2m^(2)yy_(1)` `"or "y_(2)(1+x^(2))+xy_(1)=m^(2)y` |
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