There's not a lot of information her about how long she has been going, and whether this has always been the case, but I'll try to answer as best I can.
I'm going to go with the assumption that this childcare situation is new, and that until recently you and/or her mother have been at home with her.
If that's the case, then I suspect she is experiencing a lot of separation anxiety. She's used to being with mom or dad, and I suspect the childcare provider is not well-known to her, so it seems very scary to be left alone. She might not be able to understand that you're only leaving her for a while, and may be very scared that you're never coming back.
For a child to be upset when her parents leave is quite normal, and is a good sign that she is strongly attached to you, although the reactions you describe do seem a little more extreme than I might expect on average.
There are a few things you can try that might help her cope with the separation, tide her over until you return, and help her to understand that you will always be coming back to pick her up.
If you haven't already, try to arrange a time that you can be at the childcare location with her. Either book a morning off work one day, or arrange to go in the evening or on a weekend for a bit. Spend some time there with the childcare provider and your child, which will hopefully help her to acclimatize to the location and the person, and make it a little less scary.
Give her some pictures of you, her mother, and anyone else whom she loves and who makes her feel safe. If she has a locker or other personal location, let her put them up there so she can see them any time she's feeling alone. If there is no such location, put them into a book that she can keep in her bag, or arrange with the childcare provider to keep it for her and let her see it whenever she needs.
Write a note for her every morning and put it in her snack/lunch/backpack. Let the childcare provider know, and ask them to read it to her when she pulls it out. In the note, reassure her that you love her and miss her, and look forward to seeing her at the end of the day.
One strategy that can be very powerful is to give her something of yours to hold onto for the day. It could be a (inexpensive) piece of jewelery, a coin, a favourite book, knickknack, etc. It should be something of yours, though, not a random object or one of her own possessions. I would recommend something that is not fragile and not too valuable, since a 3-year-old will not be the best at keeping it safe and may lose/break it.
The point of this is for her to have something that she can see you value, to help reassure her that you will be coming back (because you'll need to get it back from her). It also tells her that you value her, because you're trusting her to take care of it for you.
- When you are dropping her off, keep talking about what you're going to do when the two of you are together again. It doesn't really matter what you do, and doesn't need to be anything special or out of the ordinary, but focusing on the "together" time helps to bridge the time when you're away and again sends the message that you will be returning to get her.
For example, "I can't wait until we're at home and we can read stories together!" or "I'm so excited for the car ride home after I pick you up. I want to hear all about your day!"
It might also be worth talking to the childcare provider about how things go after you leave. I have seen many children that act as if the world is ending when their parents leave, but five minutes later they are happily playing as if nothing has happened. If that's the case with your daughter, there may not be too much of a problem. She's just sad to see you go, but is coping and moving on.
If she remains very upset after you leave, then hopefully the above strategies will help to mitigate that, and she can learn to cope without you while you're at work.