Find the first partial derivatives and evaluate each at the given point.
Function
w = 2x^2y − 6xyz + 10yz^2
Point
(2, 5, −3)
wx(2, 5, −3) =
wy(2, 5, −3) =
wz(2, 5, −3) =
Partials are easy. Just consider the extra variables as constants.
Wx = 4xy-6yz
Wy = 2x^2-6xz+10z^2
Wz = -6xy+20yz
Now just plug in the numbers.