Heat the oven to 375°F Lightly grease cooking sheet.
In a large bowl combine the flour, baking powder, baking soda and salt.
In the bowl of an electric mixer, cream the butter and both sugars together. Beat until smooth, about 1 minute. Add the applesauce, egg and vanilla and mix until blended about 2 minutes. Add the flour to the applesauce mixture and mix well. Remove the bowl from the mixer and stir in the oats and raisins.
Drop rounded teaspoonfuls onto the prepared baking sheets about two inches apart.
Bake until slightly golden, about 10 to 12 minutes.
Remove the baking sheets from the oven and cool on wire racks for 5 minutes. Remove the cookies and cool completely.