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).

Asked on by albery123

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)`

We’ve answered 319,812 questions. We can answer yours, too.

Ask a question