differentiate cot^2(3x+4)
I'm assuming chain rule? But I can't get the steps to work out and get a nice, simplified answer

Question

differentiate cot^2(3x+4)
I'm assuming chain rule?  But I can't get the steps to work out and get a nice, simplified answer

hartnn · Answer

chain rule is correct, you should know derivative of x^2 , cot x and 3x+4 to solve this.
if you have tried, show us what u get...

anonymous · Answer

Okay, so 2x(-csc^2)(3x+4)(3)?

hartnn · Answer

using chain rule, 
derivative of $(f(x))^2$ will be  2f(x)f'(x)
right ? you are missing the f(x) part there.

anonymous · Answer

oh, no. Okay, let me try again.
2(cotx(3x+4))(3)

anonymous · Answer

Wait wait wait. . . ugh. I know I'm getting the middle part incorrectly

hartnn · Answer

take you time, i can wait. try to get to correct answer, i will correct you incase of any error.

anonymous · Answer

so f(x) = cot^2(3x+4), which means that is equivalent to cot(3x+4)^2. 
then 2(cot(3x+4))(-3csc^2)?

hartnn · Answer

getting very close to correct answer!
you basically missed the argument of csc^2 
shouldn't it be, 
2(cot(3x+4))(-3csc^2(3x+4)) 
?
and with one simple step of simplification, you'll get the required answer.

anonymous · Answer

Oh, I see. I just derived the 3x+4 from the second part into "-3" and totally left out the rest.  Then,is the final answers -6cosssin(3x+4)?
How do I put the cos(3x+4) and the sin(3x+4) together to pull out the "(3x+4)"? @hartnn

hartnn · Answer

what?! i couldn't understand your question,
if you got this : 2(cot(3x+4))(-3csc^2(3x+4)) 
then its simplified version will be 
-6(cot(3x+4))csc^2(3x+4)
i believe this is simplified and needs no further simplification

anonymous · Answer

ohh, okay. No, that is what I got. But I thought since it had cot(3x+4) and csc^2(3x+4), maybe there was some way I can take out the (3x+4) since it was in both
But if that's as simplified as it can get, then I see I can't just pull it out

hartnn · Answer

ok, that (3x+4) is the angle (or argument) of the trigonometric function.
like $\theta$
so, say in $\cos \theta \sin^2 \theta$, you cannot factor $\theta$  and just write cos . sin^2 , in same way you cannot factor out 3x+4 here.

anonymous · Answer

OH, wow. I see, I see. that makes sense, thank you.

hartnn · Answer

welcome ^_^