In a large bowl combine water, 1 tablespoon of the sugar and the yeast. Let stand 5 minutes to dissolve yeast. With a wooden or sturdy spoon, stir in remaining sugar, sweet potato, softened butter, salt and eggs. Gradually stir in whole wheat flour and as much of the all-purpose flour as you can with the spoon.
Turn dough out onto a lightly floured surface. Knead in enough of the remaining flour to make a moderately stiff dough that is smooth and elastic (6 to 8 minutes total). Shape dough into a ball. Place in a greased bowl; turn once to grease surface of the dough. Cover; let rise in a warm place until double (about 1 hour).
Punch dough down. Turn dough out onto a lightly floured surface. Cover and let rest 10 minutes. Meanwhile, lightly grease a 13x9x2-inch baking pan.
Shape dough into 16 balls; place in prepared pan. Cover; let rise in a warm place until nearly double in size (45 minutes).
Bake in a 375 degree F oven about 20 minutes or until golden. Brush with melted butter; remove from pan. Serve warm. Makes 16 rolls.