In summary, the conversation is discussing finding the derivative of y = (csc(x) + cot(x) )^-1 using the chain rule. The person explains that letting u = csc(x) + cot(x), the derivative can be found by the formula dy/dx = (dy/du)(du/dx). They suggest simplifying u to (1+cos(x))/sin(x) and using the quotient rule to find du/dx.
darkknight, you titled this "using chain rule" and Monoxdifly just told you what that is! Are you able to do this now?
Letting u= csc(x)+ cot(x), y= u^-1. What is dy/du? What is du/dx?
chain rule: dy/dx= (dy/du)(du/dx).
If the difficulty is du/dx, it might help you to write \(\displaystyle u= csc(x)+ cot(x)= \frac{1}{sin(x)}+ \frac{cos(x)}{sin(x)}= \frac{1+ cos(x)}{sin(x)}\) and use the "quotient rule".