We consider implicit functions y = y(x) defined by a system of equations
G_i(x,y) = 0
G
i
(
x
,
y
)
=
0
, i=1,...,m. In the case of convex differentiable functions
G_i
G
i
we establish some sufficient conditions under which the component function
y_k(x)
y
k
(
x
)
is convex or concave. Examples show that without these assumptions
y_k(x)
y
k
(
x
)
can be nonconvex and nonconcave. For the special case with additive separated convex functions
G_i(x,y) = g_i(x) + h_i(y)
G
i
(
x
,
y
)
=
g
i
(
x
)
+
h
i
(
y
)
additional results concerning the gradient vectors of
g_i
g
i
and
h_i
h
i
are obtained which can be applied to the differentiable continuation of convex marginal functions in parametric optimization.