Question

Find d^2y/dx^2 in terms of x and y

x^2y^2-16x=8

Answer 1

Please use parentheses to correctly write the equation. I would be able to assist you much better.

Answer 2

Given............y.x^2.y^2 - 16x = 8

⇒x^2.y^3 -16x = 8

if f ' = dy/dx and f '' = d^2y/dx^2

then.....

2xy^3 + 3x^2.y^2.f ' - 16 = 0 .......................(1)

⇒f ' = {16 - 2x.y^3}/3x^2.y^2........................(2)

from eqn (1)

2y^3 + 6xy^2.f ' + 6xy^2.f ' + 6yx^2.f '' = 0

⇒f '' = -y^2/3x^2 - 2.f'

from eqn(2)

f '' = -y^2/3x^2 - 2{16 - 2xy^3}/3x^2.y^2

⇒ f '' = {4xy^3 - y^4 - 32}/3x^2.y^2