the differentiation of cosec x with respect to x is -cosec x cot x.?

Answer 1

Sounds 'bout right to me ☺

Think of it as (sin(x))^(-1) then d/dx = -1sin(x)^(-2) cos(x) so -1cos(x)/sin(x)² = (-1/sin(x))*(cos(x)/sin(x)) which is
-csc(x)*cot(x)


Doug

Answer 2

cosec x = 1 / sin x

Use the chain rule to differentiate:

-1 / (sin x)^2 * cos x

=

-cos x / (sin x * sin x)

Because cos x / sin x = cot x, you can simplify this as

-cot x / sin x = -cot x * cosec x

Answer 3

yep d/dx cosec x=-cosecxcotx