How can I derive CSC^2 u without using substitution?

[racer]

Homework Statement

the derivative of CSC u is CSC u times cot u times the derivative of the u
but how can I derive CSC^2 u?


2. The attempt at a solution


CSC^2 u is (CSC u)^2

The derivative is
2(CSC u)(CSC u times Cot u)(1)

another way

CSC^2 u = CSC u times CSC u
CSC u times ( CSC u Cot u )(1) + CSC u ( CSC u Cot u)(1)

Is it correct?

 

[tiny-tim]

Hi racer!

Yes they're both right!

(d/du)cosec^2(u) = 2cosec^2(u)cot(u).

You used both substitution and the product rule … they both work in this case, and either is fine.

(Though personally, I'd always go for substitution.)