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Regard y as the independent variable and x as the dependent variable and use implicit...

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albery123 | Student, Undergraduate | eNoter

Posted March 7, 2012 at 3:24 PM via web

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Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy for y*sec(x) = 5*x*tan(y).

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 7, 2012 at 3:39 PM (Answer #1)

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Given the expression `y*sec(x) = 5*x*tan(y)` the value of `dx/dy` has to be determined. Using implicit differentiation

`sec(x) + y*sec x*tan x*(dx/dy)` = `5*tan y*(dx/dy) + 5*x*sec^2 y`

=> `(dx/dy)(y*sec x*tan x -5*tan y) =5*x*sec^2 y - sec x`

=> `(dx/dy) = (5*x*sec^2 y - sec x)/(y*sec x*tan x -5*tan y)`

The derivative `dx/dy = (5*x*sec^2 y - sec x)/(y*sec x*tan x -5*tan y)`

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