InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find `(dy)/(dx)`, when: `logsqrt(x^(2)+y^(2))=tan^(-1).(y)/(x)` |
|
Answer» Correct Answer - `(x+y)/(x-y)` `(1)/(2)log(x^(2)+y^(2))=tan^(-1)((y)/(x))` `rArrlog(x^(2)+y^(2))=2tan^(-1).(y)/(x)rArr(x^(2)+y^(2))=e^(2tan^(-1)y//x)." ...(i)"` On differentiating (i) w.r.t. x, we get `2x+2y.(dy)/(dx)=e^(2tan^(-1)y//x).(2)/((1+(y^(2))/(x^(2)))).((x(dy)/(dx)-y))/(x^(2))` `rArrx+y(dy)/(dx)=(x^(2)+y^(2)).(x^(2))/((x^(2)+y^(2))).((x(dy)/(dx)-y))/((x^(2)))." [using (i)]"` `rArr x+y(dy)/(dx)=x(dy)/(dx)-y` `rArr(x-y)(dy)/(dx)=(x+y)rArr(dy)/(dx)=((x+y))/((x-y)).` |
|