# Thread: help with a trig derivative?

1. ## 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 and that .
The ratio is a constant number. Its value is

2. 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 and that .
The ratio is a constant number. Its value is
Hint: The derivative of $\displaystyle \cot x$ is $\displaystyle \csc^2 x$.

3. 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! ???

4. 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 $\displaystyle \frac{\cot(x)}{\csc^2(x)}$

5. so i would divide cscx/csc^2 (x) ? using the quotient rule????

6. 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.

7. so the answer would be csc^2(x)/csc^2(x) ????

8. 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.

9. Originally Posted by johnny4lsu
so the answer would be csc^2(x)/csc^2(x) ????
What is the derivative of $\displaystyle 3 \cot x$?

10. 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?

11. $\displaystyle \frac{d}{dx} [3 \cot{x}] = -3\csc^2{x}$

$\displaystyle \frac{-3\csc^2{x}}{\csc^2{x}} = -3$

12. thanks a bunch skeeter. that one whooped me!!!!