partial derivative problem?
if f(x,y) = ln(x/y) then find xf_x - y^2f_yy
hard to type it but it is xf subscript x - y^2 f subscript yy
as in the partial derivative of f with respect to x
and the partial derivative of f with respect to y done twice
if f(x,y) = ln(x/y) then find xf_x - y^2f_yy
hard to type it but it is xf subscript x - y^2 f subscript yy
as in the partial derivative of f with respect to x
and the partial derivative of f with respect to y done twice
Comments
Rewrite f as f(x,y) = ln x - ln y.
So, f_x = 1/x and f_y = -1/y
==> f_xx = -1/x^2, f_yy = 1/y^2, and f_xy = 0.
Hence,
x f_x - y^2 f_yy = x * (1/x) - y^2 * (1/y^2) = 1 - 1 = 0.
I hope this helps!