Question

If `x^2y+yx^2=6`, what is `(d^2y)/(dx^2)` at the point `(1,3)`?

Answer 1

`18`

Explanation:

`x^2y+yx^2 = 2x^2y = 6` if and only if

`y=3/x^2 = 3x^-2`

`dy/dx = -6x^-3`

`(d^2y)/dx^2 = 18x^-4 = 18/x^4`

At `x=1`, we have `(d^2y)/dx^2 = 18`