In this specific course, not much. I personally had no maths education beyond year 12, and only what I'd picked up along the way while reading around the subject. All the maths you'll need to know is explained thoroughly enough in the lectures. I think if you already know linear algebra, you'll have a head start - I didn't know it, and it took a bit of work to get up to speed.
There is a lot of discussion of derivatives and partial derivatives in the course, however it's entirely possible to complete the course and feel comfortable with the material without understanding derivatives. At least, it was for me =)
As for machine learning more generally, I'm certain a greater understanding of the maths behind what's going on would make you a better practitioner. I'm sure there are plenty of people currently making their living applying ML techniques without being maths experts, but I'm also sure the leaders in the ML field are maths experts.
There is a lot of discussion of derivatives and partial derivatives in the course, however it's entirely possible to complete the course and feel comfortable with the material without understanding derivatives. At least, it was for me =)
As for machine learning more generally, I'm certain a greater understanding of the maths behind what's going on would make you a better practitioner. I'm sure there are plenty of people currently making their living applying ML techniques without being maths experts, but I'm also sure the leaders in the ML field are maths experts.