I'm taking this term the course Calculus 2.

We are now dealing with multi-variable functions and started learning Differentiability.

There are a lot of notations, definitions, so I am totally lost.

I still don't really understand what a differential is - it's somehow a linear transformation, but not clear intuitively what its meaning actually is.

Partial and Directional derivatives and Gradient - What are they? What is the difference between them? What's their relation to the differential?

I looked for intuition in Stack,Quora but it didn't really help me.

Maybe some here can help me figure it out?

Thanks in advance.