# help with a trig derivative?

• Oct 4th 2008, 06:26 PM
johnny4lsu
help with a trig derivative?
I can't seem to figure this one out. Could someone please give me some assistance with it? Thanks!

Recall that https://webwork.math.lsu.edu/webwork...c12c181e91.png and that https://webwork.math.lsu.edu/webwork...1aec8e11e1.png.
The ratio https://webwork.math.lsu.edu/webwork...9ab48f6311.png is a constant number. Its value is
• Oct 4th 2008, 06:32 PM
ThePerfectHacker
Quote:

Originally Posted by johnny4lsu
I can't seem to figure this one out. Could someone please give me some assistance with it? Thanks!

Recall that https://webwork.math.lsu.edu/webwork...c12c181e91.png and that https://webwork.math.lsu.edu/webwork...1aec8e11e1.png.
The ratio https://webwork.math.lsu.edu/webwork...9ab48f6311.png is a constant number. Its value is

Hint: The derivative of $\displaystyle \cot x$ is $\displaystyle \csc^2 x$.
• Oct 4th 2008, 06:37 PM
johnny4lsu
I am still lost on this one for some reason. I used that csc x when applying the quotient rule but im getting all mixed up! ???
• Oct 4th 2008, 06:47 PM
skeeter
your notation indicates the derivative of $\displaystyle 3 \cot(x)$ ... then divide that derivative by $\displaystyle \csc^2(x)$

it is not the derivative of the ratio $\displaystyle \frac{\cot(x)}{\csc^2(x)}$
• Oct 4th 2008, 06:53 PM
johnny4lsu
so i would divide cscx/csc^2 (x) ? using the quotient rule????
• Oct 4th 2008, 06:56 PM
ThePerfectHacker
Quote:

Originally Posted by johnny4lsu
so i would divide cscx/csc^2 (x) ? using the quotient rule????

No because the derivative symbol is only on the numerator. So you apply it only to the numerator. If the derivative symbol included the entire fraction then you would use the quotient rule.
• Oct 4th 2008, 06:58 PM
johnny4lsu
so the answer would be csc^2(x)/csc^2(x) ????
• Oct 4th 2008, 07:05 PM
ThePerfectHacker
Quote:

Originally Posted by johnny4lsu
so the answer would be csc^2(x)/csc^2(x) ????

No $\displaystyle 3\csc^2 x/ \csc^2 x = 3$.
Do not forget the factor of three.
• Oct 4th 2008, 07:06 PM
icemanfan
Quote:

Originally Posted by johnny4lsu
so the answer would be csc^2(x)/csc^2(x) ????

What is the derivative of $\displaystyle 3 \cot x$?
• Oct 4th 2008, 07:11 PM
johnny4lsu
Quote:

Originally Posted by ThePerfectHacker
No $\displaystyle 3\csc^2 x/ \csc^2 x = 3$.
Do not forget the factor of three.

I tried 3 and it is not working?
• Oct 4th 2008, 07:16 PM
skeeter
$\displaystyle \frac{d}{dx} [3 \cot{x}] = -3\csc^2{x}$

$\displaystyle \frac{-3\csc^2{x}}{\csc^2{x}} = -3$
• Oct 4th 2008, 07:22 PM
johnny4lsu
thanks a bunch skeeter. that one whooped me!!!!