Question

What is `(dy)/(dx)` of `sqrt(y/x)+sqrt(x/y)=sqrta???`

Answer 1

I am confused something still I answered.

Explanation:

• I took `a` as constant.
• Used the rule `ul(bar(|color(red)(d/(dx)(uv)=(v cdot (du)/(dx)-v cdot (dv)/(dx))/v^2))|`

Answer 2

See below.

Explanation:

Making `y = lambda^2 x` and substituting

`lambda+1/lambda = sqrta` or

`lambda^2-sqrta lambda + 1 = 0`

now solving for `lambda`

`lambda =1/2( sqrta pm sqrt(a-4))` so

`y/x = 1/4( sqrta pm sqrt(a-4))^2`

and then

`dy/dx = 1/4( sqrta pm sqrt(a-4))^2`

for `a > 4`

Attached a plot for

`sqrt(y/x)+sqrt(x/y) = 2.3`