Question

I have another derivative question, this time involving the chain rule. Can anyone help me?

Answer 1

?

Answer 2

\[(\sin x/1+\cos x)^{2}\]
They want me to solve this using the chain rule, but I'm not really sure how to go about it.

Answer 3

\[\left(\frac{\sin(x)}{1+\cos(x)}\right)^2\]?

Answer 4

Yes! That's the question.

Answer 5

you are going to take the derivative of the square first,
the derivative of the squaring function is the doubling function, so the first thing you write is
\[2\left(\frac{\sin(x)}{1+\cos(x)}\right)\times \frac{d}{dx}\left(\frac{\sin(x)}{1+\cos(x)}\right)\] but you still have to take the derivative of that quotient, and there is no way to do with without the quotient rule

Answer 6

you need help with that part or is that one ok?

Answer 7

there is a way to do it without quotient rule, but for that u need to be strong in trigonometry....

Answer 8

I understand the first part, so now for the second part, the quotient rule is really all I have to do?

Answer 9

yes

Answer 10

Let me work it out, then I'll send you my answer and you can tell me if it's right!

Answer 11

i mean "all" is not how i would put it because the quotient rule is kind of a drag, but yes, that is what you have to do

Answer 12

Haha, definitely a drag. I think I've got it though. Is the answer going to be pretty long for this one?

Answer 13

well not really
there is a raft of cancellation in the numerator i think
just grind it out, it is not that bad

Answer 14

OH!! Oh my goodness, I see what you mean. Is this it?
\[\frac{ 2\sin (x) }{ (1+\cos (x))^{2} }\]

Answer 15

yes

Answer 16

Thank you so much! I'll probably be asking another similar question shortly, but thank you for helping me with this one :)

Answer 17

your welcome, hope the hurricane passed you by

Answer 18

It did, thank goodness! I'm completely down south, so it didn't affect me at all, but I feel so terrible for everyone up north! I hope you weren't affected either!

Answer 19

power went out for like 2 second, but all around was chaos, just not right where i live
same thing happened with irene
just lucky twice i guess

Answer 20

\[5\cot \(\frac{ 2 }{ x })\]
Is the answer to ^^ that
\[10x ^{-2}\csc ^{2}(\frac{ 2 }{ x })\] ?

Answer 21

Wow! Lucky indeed! I hope everyone else can make a speedy recovery, but the damage looked pretty extensive :/

Answer 22

thats correct.

Answer 23

Sweet! Thank you :)