If z = f(x,y) and x^2 + 2xz - 2yz^2 = 10....?

If #z=f(x,y)# and #x^2 + 2xz -2yz^2 = 10#, find #(del^2z)/(delx^2)# at #(2, -1, 1)#.

1 Answer
Dec 24, 2017

#1/4#

Explanation:

#(delz)/(delx) => 2x + 2(z+x(delz)/(delx)) - 4yz(delz)/(delx)#
so, #(delz)/(delx) = (2x+2z)/(4yz-2x)#

#(del^2z)/(delx^2) => 2 + 2(delz)/(delx) + 2(delz)/(delx) - 4y(del^2z)/(delx^2)#
so, #(del^2z)/(delx^2) = (2 + 4((2x+2z)/(4yz-2x)))/(4y)#

#(del^2z)/(delx^2) = (2-3)/(4*-1) = 1/4#