Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9 inch round pan. Sift together flour, baking soda, baking powder, cinnamon and salt. Set aside.
In a large bowl, cream together the butter, white sugar and brown sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Beat in the flour mixture, mixing just until incorporated. Stir in carrots, pineapple and chopped nuts.
Pour batter into a 9 inch pan. Bake in the preheated oven for 1 hour and 15 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool.