How can you differentiate xe^x csc x without using the product rule?

[r_swayze]

I don't really know how to even start this problem because I don't think the product rule would work here since there are three variables, right?

Here is my attempt at it:

xe^x csc x

xe^x csc x + xe^x (-csc x cot x)

xe^x (csc x - csc x cot x)

Used the product rule and that's what I came up with, can anyone give me a hint at what the first step is at least?

 

[Dick]

You can easily extend the product rule to three terms. (fgh)'=f'gh+fg'h+fgh'.

 

[r_swayze]

thanks, that makes a lot more sense :)