I use a tiny bit of Mr. Clean and a microfibre (Norwex) cloth every couple of weeks.

Here is a tip I got from the home decor forum - switch to liquid body wash rather than bar soap. Your tub will be much easier to clean and stay clean longer.

We had the identical toto tub and it began to look really dingy especially those non-slip circles. It was very hard to clean. We had a bit of a disaster in the house and insurance paid for a replacement tub. I switched to the body wash and this tub has been pristine and so much easier to clean.