Question

* Derivative of Implicit functions
x + √x.y + y =1​

Answer 1

Step-by-step explanation:

Given x+√xy +y=1

Differentiate w.r.t.x

1+1/2√xy (x dy/dx +y 1)+dy/dx =0

Or (1+y/2√xy)+dy/dx (1+x/2√xy) =0

Or dy/dx =-(1+y/2√xy)/(1+x/2√xy)

Or dy/dx =-(1+√y/2√x)/(1+√x/2√y)

Or dy/dx =-(2√x+√y)(2√y+√x) /4√xy