Question

How do you determine dy/dx given `x^2+y^2=1.1`?

Answer 1

`dy/dx=color(green)(-x/y)`

Explanation:

If `x^2+y^2=1.1`
then
`color(white)("XXX")(d(x^2+y^2))/(dx)=(d(1.1))/(dx)`

`color(white)("XXX")rarr (dx^2)/(dx)+(dy^2)/dx=0`

`color(white)("XXX")rarr 2x+(dy^2)/(dy) * (dy)/(dx) = 0`

`color(white)("XXX")rarr 2x+2y * (dy)/(dx)=0`

`color(white)("XXX")rarr 2y * (dy)/(dx)=-2x`

`color(white)("XXX")rarr (dy)/(dx)=-x/y`