How do you use the quotient rule to find the derivative of X?

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How do u tak the derivative of

X = (cos@)/(sin@)
dx/d@ = ?
 
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Two suggestions:

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

second: use ordinary derivative tools for trig functions
 


must I merely memorize the derivate of cotangent?
 


Maxwellkid said:
must I merely memorize the derivate of cotangent?

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...
 


Use the product rule or the quotient rule.
 


Isn't derivative of cotangent equal to csc squared?
 


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


Where do i start to derive it?
 


Alright, I'll start you off . . .

cot(x) = \frac{cos(x)}{sin(x)}[/itex]<br /> <br /> \frac{d(cot(x))}{dx} = \frac{d}{dx} \left (\frac{cos(x)}{sin(x)} \right )<br /> <br /> Now, can you remember the rule for differentiating the quotient of two functions?
 
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Try checking using the quotient rule:

\left({f \over g}\right)&#039; = {f&#039;g - fg&#039; \over g^2}, \qquad g \ne 0

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

Regards.
 

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