Differentiation help please?

Question

Differentiate the following function of x (using either the product, quotient or chain rule)

f(x) = cosec(x+1)

Thanks in advance :) 10pts to first correct answer with clear working :)

Answer 1

f(x) = 1 / sin (x+1)

Using quotient rule:

df / dx = cos (x+1) / sin^2 (x+1) = cosec x · cotan x