Basic Derivative: ln[(sin(x)^3)^3] - Is it Correct?

[RJC]

Alright, here is the equation:

ln [(sin(x)^3)^3]

And here is my answer with some steps, please tell me if I'm wrong..

9 ln(sin'x)

9 (cos'x)/(sin'x)

Derivative= 9tan(x)^-1

is that correct?

 

[mathmike]

I Get 9*x^2*cot(x^3)
It Looks Like U Forgot The X^2 Term When You Got The Der Of X^3

 

[Jameson]

Usually we say that \frac{1}{\tan(x)}=\cot(x). Looks good to me.

 

[RJC]

soo.. which answer is correct? the whole sin'x is cubed, not just the x value within the sine..

 

[Jameson]

I see nothing wrong with your original answer, except for a better notation.

 

[RJC]

so 9cot(x) would be a better answer?

 

[Jameson]

Yes, it's more concise and very standard.