Find `(d^2y)/(dx^2)` if `x^2-2y^2=3`

Expert Answers
justaguide eNotes educator| Certified Educator

The variables x and y are related by `x^2-2y^2=3` .

Taking the derivative of both the sides with respect to x,

`2x - 4y*(dy/dx) = 0`

=> `dy/dx = x/(2y)`

The second derivative `(d^2y)/(dx^2) = (2y - 2*x*(dy/dx))/(4y^2)`

= `(2y - 2x*(x/(2y)))/(4y^2)`

= `(2y - x^2/y)/(4y^2)`

= `1/(2y) - x^2/(4*y^3) `

The required derivative `(d^2y)/(dx^2) = 1/(2y) - x^2/(4*y^3)`

pramodpandey | Student


Differentiate with respect to x (implicitly)



`(dy)/(dx)=(1/2)xy^(-1)`       (ii)

differentate again w.r.t x






oldnick | Student


expliciting respect y:




Black line:  y(x)

Red line:   y'(x)

Blue line: y''(x)