InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
`"If "log(x^(2)+y^(2))=2tan^(-1)""((y)/(x))," show that "(dy)/(dx)=(x+y)/(x-y)` |
|
Answer» Differentiating both sides w.r.t. x, we get `(d)/(dx){log(x^(2)+y^(2))}=2(d)/(dx){tan^(-1)((y)/(x))}` `"or "(1)/(x^(2)+y^(2))xx(d)/(dx)(x^(2)+y^(2))=2(1)/(1+(y//x)^(2))xx(d)/(dx)((y)/(x))` `"or "(1)/(x^(2)+y^(2)){(d)/(dx)(x^(2))+(d)/(dx)(y^(2))}=2xx(x^(2))/(x^(2)+y^(2)){(x(dy)/(dx)-yxx1)/(x^(2))}` `"or "(1)/(x^(2)+y^(2)){2x+22y(dy)/(dx)}=(2)/(x^(2)+y^(2)){x(dy)/(dx)-y}` `"or "{x+y(dy)/(dx)}=2{x(dy)/(dx)-y}` `"or "x+y(dy)/(dx)=x(dy)/(dx)-y` `"or "(dy)/(dx)(y-x)=-(x+y)` `"or "(dy)/(dx)=(x+y)/(x-y)` |
|