InterviewSolution
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InterviewSolution
| 1. |
`y^(x) = x^(y)` then find dy/dx |
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Answer» `y^(x) = x^(y)` `rArr "log" (y^(x)) = "log"(x^(y))` `rArr x"log"y = y"log"x` Differentiate both sides w.r.t.x `x * (d)/(dx) "log" y + "log" y * (d)/(dx)x` `= y * (d)/(dx)"log"x + "log"x * (d)/(dx)y` `rArr (x)/(y)(dy)/(dx) + "log" y * 1 = (y)/(x) + "log"x (dy)/(dx)` `rArr ((x)/(y) - "log"x)(dy)/(dx) = (y)/(x) - "log" y` `rArr (x-y "log"x)/(y) (dy)/(dx) = (y-x "log"y)/(x)` `rArr (dy)/(dx) = (y)/(x) * (y-x"log"y)/(x-y"log"x)` |
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