how do you find the derivative of 3csc2x

Question

psymon · Answer

This would be chain rule. You have two layers that you need to take the derivative of. First you have csc(   ) and then you have the inner layer 2x. Chain rule is when you multiply the derivatives of all the layers you have. Can you see what I mean by saying that csc(   ) would be an outer layer and 2x would be an inner layer?

anonymous · Answer

yeah, but what about the three?

psymon · Answer

Coefficients just tag along. They don't affect the derivative itself, they just might get multipliedor divided along the way.

psymon · Answer

So what you need the derivative of first is the outer portion, which is csc. Do you know the derivative of csc?

anonymous · Answer

yeah isnt it -cscxcotx

psymon · Answer

Right. Now we just multiply by the derivative of what was inside of csc.

anonymous · Answer

so multiply by 2?

psymon · Answer

Yep :3

anonymous · Answer

and then what do you do with the three

psymon · Answer

It just gets multiplied by the 2. Like I said, the constants, whether being multiplied or divided, just kinda tag along.

anonymous · Answer

so the answer is -6cscxcotx??

psymon · Answer

-6csc(2x)cot(2x) would be your answer.

anonymous · Answer

ooh

anonymous · Answer

okay

psymon · Answer

Well, that was the next point I was going to bring up. Whatever is inside of each layer does not change.

psymon · Answer

I tend to explain this in a little bit of a unique way, so do you mind if I show you another example?

anonymous · Answer

well i can always ask my teacher monday, i just wanted to have a sort of idea because i forgot most of it from last year haha; thanks though (:

psymon · Answer

Oh xD Lol, alright, np then. Good luck :3