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

2 Answers
Mar 3, 2018

I am confused something still I answered.

Explanation:

My notebook...

  • 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))|#
Mar 3, 2018

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#

enter image source here