We'll have to calculate partial derivative for given
expression.
We'll calculate
dz/dx.
z=3x^2-2y^2+2xy
We'll
differentiate the expression of z with respect to x, treating y as a
constant.
dz/dx =
(d/dx)(3x^2-2y^2+2xy)
dz/dx = 3(d/dx)(x^2) - 2y^2(d/dx)(1)
+ 2y(d/dx)(x)
dz/dx = 6x +
2y
Now, we'll differentiate z with respect
to y, treating x as a constant.
dz/dy =
(d/dy)(3x^2-2y^2+2xy)
dz/dy = 3x^2(d/dy)(1) - 2(d/dy)(y^2)
+ 2x(d/dy)(y)
dz/dy = 0 - 4y +
2x
dz/dy = 2x -
4y
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