Partial Derivatives and Computing Them Algebraically

I have actually never been exposed to the concept of partial derivatives before and was confused when the books definition of a partial derivative contained limits. I thought this class wasn't planning on using limits??? Also i don't think the purpose of a partial derivative is explained either? Is it just a fraction of a rate of change?

Perhaps the class will have the most difficulty with second-order partial derivatives, especially if the concept of partial derivatives was difficult to begin with. But what I did like about these sections were familiar examples used to try and explain this type of function.