# X = (cos@)/(sin@)

1. Aug 16, 2009

### Maxwellkid

How do u tak the derivative of

X = (cos@)/(sin@)
dx/d@ = ????

2. Aug 16, 2009

Re: Derivative

Two suggestions:

first: regardless of the variable name, what function does cosine over sine reduce to?

second: use ordinary derivative tools for trig functions

3. Aug 16, 2009

### Maxwellkid

Re: Derivative

must I merely memorize the derivate of cotangent?

4. Aug 16, 2009

Re: Derivative

Well, you should know how to use ALL of the derivative methods you encounter, so you don't have to re-derive them each time you need them. On the plus side: if you take enough math courses learning them will be natural. Good luck in your studies................

5. Aug 16, 2009

### CaffeineJunky

Re: Derivative

Use the product rule or the quotient rule.

6. Aug 16, 2009

### Maxwellkid

Re: Derivative

Isn't derivative of cotangent equal to csc squared???

7. Aug 16, 2009

### jgens

Re: Derivative

Why don't you try deriving it to check ;-)

8. Aug 16, 2009

### Maxwellkid

Re: Derivative

Where do i start to derive it?

9. Aug 16, 2009

### jgens

Re: Derivative

Alright, I'll start you off . . .

$$cot(x) = \frac{cos(x)}{sin(x)}[/itex] [tex]\frac{d(cot(x))}{dx} = \frac{d}{dx} \left (\frac{cos(x)}{sin(x)} \right )$$

Now, can you remember the rule for differentiating the quotient of two functions?

10. Aug 17, 2009

### Дьявол

Re: Derivative

Try checking using the quotient rule:

$$\left({f \over g}\right)' = {f'g - fg' \over g^2}, \qquad g \ne 0$$

In your case f=cos@ and g=sin@

Regards.