Question

For the following functions find the gxy, gxx, gyyand gyx

g(x, y) = x2 + 3xy 7y + cos(5x)

Answer 1

gx = $(del"g")/(delx) = 2x + 3y - 5 sin(5x)$

gy = $(del"g")/(dely) = 3x - 7$

gxx = $2 - 25 cos(5x)$

gyy = 0

gxy = $del/(delx) ((del"g")/(dely))$

= $del/(delx) (3x - 7)$

= 3

gyx = $del/(dely) ((del"g")/(delx))$

= $del/(dely) (2x + 3y - 5 sin(5x))$

= 3