implicit differentiation to find second derivative

if sqrt(x) + sqrt(y) = 1 find y"
differentiate the given expression w.r.t.x and do not forget to add dy/dx when differentiating
y w.r.t.x simplify and extract the value of dy/dx

differentiate that again w.r.t.x and do not forget to add dy/dx when differentiating
y w.r.t.x , use the earlier value for dy/dx for substitution

other questions
if √(xy) = x - 2y, find dy/dx ---------------->( implicit differentiation )

if xy + y^2 =1 , find dy/dx ---------------- implicit differentiation


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second derivative at a given point with implicit differentiation

if x² +y² = 25, find the value of d²y / dx² at (4,3)
differentiate once , extract the value of dy/dx
find the value at (4,3)
differentitate the expression for dy/dx once more
to get d²y / dx²
it might contain dy/dx
substitute (4,3) and the value obtained earlier for dy/dx

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