The definition of the curl of a vector field ( F = < f, g, h> ) is given by:

Curl of F = (gradient) x F = (dh/dy - dg/dz)i + (df/dz - dh/dx)j + (dg/dx - df/dy)

This is what is in my textbook and is the definition I have consistently found online. My question is why is the j component not negative, as is normally done when computing cross product?