Differentiate question?

Question

Differentiate http://img80.imageshack.us/img80/7605/olocapnlhj6caijxsczcaknaa1.png

Answer 1

y = csc @(cot @ + @)
by the product rule, that's
(csc @)'(cot @ + @) + (csc @)(cot @ + @)' =
(-csc @ cot @)(cot @ + @) + (csc @)(-csc^2 @ + 1) =
you can multiply this out if you want or if your teacher requires, I get ...
(-csc @ cot^2 @) - @csc@ cot@ - csc^3 @ + csc @
or you can leave it in factored form as in the second last step

Answer 2

y=cscx(cotx+x);

put x(cotx+x)=t

then diff t=x(cotx+x) and try the product method